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2.4.8 - Bowers' -illions

 
Polytwister Image Created by Jonathan Bowers
(Used with Permission)

2.4.8
Jonathan Bowers'
4 Tiered -illion Series
 
 
 
Jonathan Bowers
 
    Jonathan Bowers is both an infamous large number enthusiast and polychorist. Like many other amateur mathematicians who have devoted some of their mathematical expertise to generating large numbers, we will be talking about his work quite a lot. In fact Bowers is an exceptional case, and we will have a lot to talk about in the coming section on his work.
 
    Jonathan Bowers is probably best known for his extremely large numbers, and array notation, which he uses to define them. However, we won't be getting into these subjects until at least section III, as these are more advanced  topics. He is also known for working with polytopes, which are higher dimensional solids. In addition to these achievements he has also created about a hundred -illion style numbers, which we will call the "Bowers Milestone -illions".
 
    Unlike the systems of Professor Henkle, Conway&Guy and others, Bowers creates a utterly vast system; much more vast than any of the others yet introduced. However he leaves us to construct the intermediate terms.

    I contacted him to ask him about his system. He stated that he was more interested in the "milestones" than the intermediate terms. He felt that this could be worked out by those who were interested in the details. This is not that different than the approach taken by Professor Henkles and Mr. Ondrejka when they provided lists for numbers but left the intermediates out. Unlike Professor Henkles system however, Bowers system extends way way beyond the millionth illion. His system is so vast in fact that no complete table could ever be constructed. As we will see, the intermediates for Bowers system are far more complex than anything we have previously encountered.
 
    It should also be noted that Bowers has actually tweaked his list of names at least once. There was an old list of -illions on his older site (now defunct) which differs slightly from his new list. The only difference is in the names he chooses, and how far he extends the system. His new system extends another "tier" beyond his old system. What does that mean? Read on and find out.
 
Bower's Milestone -illions
 
    Bower's devotes a single web page to his milestone -illions on each of his websites. His old system can be found on his old site. Unfortunately his old site was abandoned quite a few years ago and the service provider eventually terminated it along with all other websites made with AOL hometown. Luckily the website was archived by another server, so that technically his old site can still be found online. The archived web page of Bower's old style illions can be found here:

http://web.archive.org/web/20071205035836/members.aol.com/hedrondude/numbers.html

    Bower's eventually moved his site to a different location sometime around 2007. His new site also contains a list of -illion numbers, almost identical to his original list. Some additions were made, and some of the names were changed. His new -illion list can be found here:

    We will be considering both his old and new system simultaneously since they are essentially the same system. Bowers list of milestone members of his -illion system begins with the established -illions. Namely, a million, billion, trillion, ... all the way up to vigintillion. In other words, the first 20 -illions are taken as canon. Next Bowers list begins to jump to the 30th -illion, then the 40th, 50th, ... and so on all the way to the 100th -illion. Next he jumps to the 200th, 300th, 400th, ... all the way to the 1000th -illion, which Bower's coins a millillion. Bowers says he came up with this name independently and later discovered others had chosen it to represent the 1000th -illion. With the exception of the millillion, every other name below this is more or less a reiteration of the Conway&Guy system, with some minor differences. The spellings are almost identical to the Conway&Guy spellings, with only slight alterations.

    After the millillion we start getting into unique number names of Bowers own invention. Next he calls the 1,000,000th -illion a " micrillion ". The only other "recognized" name for this is the milli-millillion from Henkles naming scheme. Bowers reasoned that since "milli" is also an SI prefix for 1/1000, he could use the SI prefix "micro" (1/1,000,000) to represent the 1,000,000th -illion. This allowed him to follow up with a nanillion, 10^(3,000,000,003), a picillion, 10^(3x(10^12)+3), a femtillion, 10^(3x(10^15)+3), an attillion, 10^(3x(10^18)+3), a zeptillion, 10^(3x(10^21)+3), and lastly a yoctillion, 10^(3x(10^24)+3). Recall the SI prefixes milli, micro, nano, pico, femto, atto, zepto, and yocto from Chapter 2-2. The problem is that there are no official SI prefixes beyond this point. To continue Bowers opts to transition, somewhat haphazardly, from SI prefixes into a greek based system. However, he chooses to change the offset used in the short scale, and instead the number in greek represents 1000 raised to that number. This is in contrast to the short scale where a latin number represents 1000 raised to that number + 1.

    Bower's invents the term xonillion for 10^(3x(10^27)+3), presumably by inventing an additional small scale SI prefix such as "xono". With prefixes exhausted Bower's switches to a system suggestive of greek. His next term is vekillion, which seems to come from "deka", the greek word for ten. After this he follows a similar pattern used to reach the millillion, except this time the greek is indicating the power of a thousand multiplied by 3 in the 2nd exponent. Eventually he exhausts greek once he reaches a killillion for 10^(3x(10^3000)+3), from "kilo", greek for "thousand". Reaching this point can be thought as reaching the end of a kind of second tier, just as reaching a millillion was like reaching the end of the first tier. I sometimes refer to these as "levels".

    Now "kilo" is also the SI prefix for 1000. Bowers therefore decides to continue by using the large scale SI prefixes to construct his next series of illions. Next we have megillion, gigillion, terillion, petillion, exillion, zettillion, and yottillion. After this we again run out of official SI prefixes, so Bowers invents one so we can have a xennillion.

    The next step is a point of divergence from his old to new system. In his old system Bowers, having run out of latin and greek, opts to use english numbers to continue up to the next tier with names like twentillion, hundrillion, and thousillion. In his new system he scraps the english names and opts for a special numbering system of his own invention. Bowers had created a series of special names for polytopes of various dimensions. For example, we call 2-d figures polygons, and 3-d figures polyhedrons. Polychorists study higher dimensional analogies of these figures, and all of these figures are collectively known as polytopes. Because there was no codified system of names for figures in higher dimensions Bowers invented one. In the polychorist community it is generally accepted that 4-dimensional figures should be called polychorons. This however is not recognized in professional circles, and is used mainly by amateur mathematicians who study these objects. Bowers continued these names with 5-d figures being called polyterons, 6-d figures called polypetons, 7-d figures called polyectons, 8-d figures called polyzettons, 9-d figures called polyyottons, etc. From these suffixes bowers derives a whole series of milestone -illions. Amazingly Bowers had extended his polytope suffixes all the way up to the tredecillionth member! This is particularly insane because no human being or current computer can hope to cope with a tredecillion dimensions! In any case, this does allow Bowers to surpass the 3rd tier and enter the next "level" beyond a thousillion. Bower's however does not manage to reach the end of the 4th tier.

    In his original system he only gets up to hyper-hyper-exponential class numbers ( as defined by my number ranges described in the article "number ranges"). In his newer system he goes up to lower hyper-hyper-hyper-exponential numbers. I also refer to "hyper-exponents" as "2nd exponents", and growth rates of this kind "exponential exponential growth" or "double exponential growth". "Hyper-hyper-exponents" are "3rd exponents", and growth rates of this kind are "exponential exponential exponential growth" or "triple exponential growth", and so on. Each time we go up another exponent in a power tower, we are going up one "level" , "tier" , or "plateau" in an illion series. Thus we can say Bowers original system reaches the level of triple-exponents (ie. 10^10^10^N) while his newer system reaches one level higher with quadruple-exponents (ie. 10^10^10^10^N). Hence, we can characterize Bowers system as a "quadruple-exponential" illion series. Note that, in comparison Conway & Guys system can only be treated as a "double-exponential" illion series, since it would require exponentially long names in their system to describe triple-exponential illion names, double exponentially long names to describe quadruple-exponential illions, and so on.
 
    The best way to introduce Bowers -illions is probably to provide the list of his milestone illions, more or less as they appear on his website. Although this list can be found on many other websites verbatim, this is my site, and I'm a bit of a completist :)

    Unlike other presentations however, we will be reviewing the system and considering the possibility of filling in the gaps and what its limits of extension are.

    The following table includes every number that Bowers lists on his -illions pages that is intended as part of his system (his list also includes a few extra names outside of his system for comparison. I will include these in a separate table). These values will be presented in scientific-E notation, where nEm = n * 10^m. Please note that the order of operations will be as follows:

1. All operations within paranthesis resolved first

2. E-notation takes precedence over all other operations

3.Multiplications are carried out from left to right

4. Additions and subtractions are resolved from left to right


    Unfortunately Bowers -illions are so large that it is advantageous to have a more compact notation than even Scientific-E notation. For the purposes of -illion numbers I have a series of "prefix functions". I will explain these later in more detail. Specifically we will be using my short scale function:

Let H(n) = 1E(3n+3)

where n is an element of the set { 0,1,2, ... }


    The H here stands for "half scale". The reason I use this instead of S(n) for "Short scale" is because I already use S(n) for the "successor function", one of the four fundamental functions. We'll learn what those are in chapter 3-1. The advantage of the H-function is that the number "n" indicates the prefix attached to the -illion in the short scale. For example, an octillion is equal to H(8) = 1E(3*8+3) = 1E(24+3) = 1E27. This is because "oct-" is latin for 8.

    Because Bowers changes some of his names I have decided to list both his old and new Nomenclature in a single table. If there is a dash, it means that there isn't a name for that number in that nomenclature. For example, Bowers had no name for a myrillion in his old system. If there is a quotation mark this means the name is the same as in the other system. This makes it easier to see where Bowers has made changes. Only names that have been changed will have rows with two names listed. In every way Bowers new system is an expansion of his old. Not only does it extend out further, but he provides more intermediates than before, and more numbers outside of his system. Thus every number in the old system is included in the new, but not every new number has an equivalent in the old system. Number names in red and italics are numbers that can not properly be attributed to Bowers, even though they appear on his list. This mainly applies to all of the names under a millillion. Bowers most likely got these names from the Conway&Guy system, and they barely differ at all from them. None the less they are included for you inspection.

 So Here is Jonathan Bowers complete list of "milestone" illions:

Jonathan Bowers' Milestone illion Series

 Old Nomenclature
New Nomenclature
Scientific E Notation
Half-Scale Notation
 million  "
 1,000,000 H(1)
 billion "
 1,000,000,000 H(2)
 trillion  "  1,000,000,000,000  H(3)
 quadrillion  "  1,000,000,000,000,000  H(4)
 quintillion  "  1,000,000,000,000,000,000  H(5)
 sextillion  "  1,000,000,000,000,000,000,000  H(6)
 septillion  "  1,000,000,000,000,000,000,000,000  H(7)
 octillion  "  1E27
 H(8)
 nonillion  "  1E30
 H(9)
 decillion  "  1E33  H(10)
 undecillion  "  1E36  H(11)
 doedecillion  "  1E39  H(12)
tredecillion
 "  1E42  H(13)
 quattuordecillion  "  1E45  H(14)
 quindecillion  "  1E48  H(15)
 sexdecillion  "  1E51  H(16)
 septendecillion  "  1E54  H(17)
 octodecillion  "  1E57  H(18)
 novemdecillion  "  1E60  H(19)
 vigintillion  "  1E63  H(20)
 trigintillion  "  1E93
 H(30)
 quadragintillion  "  1E123  H(40)
 quinquagintillion  "  1E153  H(50)
 sexagintillion  "  1E183  H(60)
 septuagintillion  "  1E213  H(70)
 octogintillion  "  1E243  H(80)
 nonagintillion  "  1E273  H(90)
 centillion  "  1E303  H(100)
 -  cenuntillion  1E306  H(101)
 -
 duocentillion  1E309  H(102)
 -
 centretillion  1E312  H(103)
ducentillion
 " 1E603
H(200)
 trecentillion  "  1E903  H(300)
 quadringentillion  "  1E1203  H(400)
 quingentillion  "
1E1503
H(500)
 sescentillion  "  1E1803  H(600)
 septingentillion  "  1E2103  H(700)
 octingentillion "
 1E2403  H(800)
 nongentillion  "  1E2703  H(900)
millillion
"
1E3003
 H(1000)
 - myrillion
 1E30,003 H(10,000)
 micrillion "
1E3,000,003
 H(1,000,000)
nanillion
"
1E3,000,000,003
H(1,000,000,000)
 picillion "
1E3,000,000,000,003
H(1,000,000,000,000)
 femtillion "
1E3,000,000,000,000,003
H(H(4))
attillion
 "  1E3,000,000,000,000,000,003 H(H(5))
 zeptillion  "  1E3,000,000,000,000,000,000,003  H(H(6))
 yoctillion  "  1E3,000,000,000,000,000,000,000,003  H(H(7))
 xonillion "
1E(3E27+3)
H(H(8))
 vecillion "
1E(3E30+3)
 H(H(9))
 mecillion  "  1E(3E33+3) H(H(10))
 duecillion  " 1E(3E36+3)
H(H(11))
 trecillion  "  1E(3E39+3)  H(H(12))
 tetrecillion  "  1E(3E42+3)  H(H(13))
 pentecillion  "  1E(3E45+3)  H(H(14))
 hexecillion  "  1E(3E48+3)  H(H(15))
 heptecillion  "  1E(3E51+3)  H(H(16))
 octecillion  "  1E(3E54+3)  H(H(17))
 ennecillion  "  1E(3E57+3)  H(H(18))
 icosillion  "  1E(3E60+3)  H(H(19))
 triacontillion  "  1E(3E90+3)  H(H(29))
 tetracontillion  "  1E(3E120+3)  H(H(39))
 pentacontillion  "  1E(3E150+3)  H(H(49))
 hexacontillion  "  1E(3E180+3)  H(H(59))
 heptacontillion  "  1E(3E210+3)  H(H(69))
 octacontillion  "  1E(3E240+3)  H(H(79))
 ennacontillion  " 1E(3E270+3)
H(H(89))
 hectillion  "  1E(3E300+3)  H(H(99))
 killillion  "  1E(3E3000+3)  H(H(999))
 megillion  "  1E(3E3,000,000+3)  H(H(999,999))
 gigillion  "  1E(3E3,000,000,000+3)  H(H(999,999,999))
 terillion  "  1E(3E3,000,000,000,000+3)  H(H(999,999,999,999))
 petillion  "  1E(3E3,000,000,000,000,000+3) H(H(H(4)-1))
 exillion  "  1E(3E3,000,000,000,000,000,000+3)  H(H(H(5)-1))
 zettillion  "  1E(3E3,000,000,000,000,000,000,000+3)  H(H(H(6)-1))
 yottillion  "  1E(3E(3E24)+3)  H(H(H(7)-1))
 xennillion  "  1E(3E(3E27)+3)
 H(H(H(8)-1))
 vekillion  dakillion  1E(3E(3E30)+3)  H(H(H(9)-1))
 mekillion  hendillion 1E(3E(3E33)+3)
H(H(H(10)-1))
 duekillion  dokillion  1E(3E(3E36)+3)  H(H(H(11)-1))
 trekillion  tradakillion  1E(3E(3E39)+3)  H(H(H(12)-1))
 tetrekillion  tedakillion  1E(3E(3E42)+3)  H(H(H(13)-1))
 pentekillion  pedakillion  1E(3E(3E45)+3)  H(H(H(14)-1))
 hexekillion  exdakillion  1E(3E(3E48)+3) H(H(H(15)-1))
 heptekillion  zedakillion  1E(3E(3E51)+3)  H(H(H(16)-1))
 octekillion  yodakillion  1E(3E(3E54)+3)  H(H(H(17)-1))
 ennekillion  nedakillion  1E(3E(3E57)+3)  H(H(H(18)-1))
 twentillion  ikillion  1E(3E(3E60)+3)  H(H(H(19)-1))
 -  ikenillion  1E(3E(3E63)+3)  H(H(H(20)-1))
 -  icodillion  1E(3E(3E66)+3)  H(H(H(21)-1))
 triatwentillion ictrillion
 1E(3E(3E69)+3)  H(H(H(22)-1))
 -  icterillion  1E(3E(3E72)+3)  H(H(H(23)-1))
 -  icpetillion  1E(3E(3E75)+3)  H(H(H(24)-1))
 -  ikectillion  1E(3E(3E78)+3)  H(H(H(25)-1))
 - iczetillion
 1E(3E(3E81)+3)  H(H(H(26)-1))
 -  ikyotillion  1E(3E(3E84)+3) H(H(H(27)-1))
 -  icxenillion  1E(3E(3E87)+3)  H(H(H(28)-1))
 thirtillion  trakillion  1E(3E(3E90)+3)  H(H(H(29)-1))
 fortillion  tekillion  1E(3E(3E120)+3)  H(H(H(39)-1))
 fiftillion  pekillion  1E(3E(3E150)+3)  H(H(H(49)-1))
 sixtillion  exakillion  1E(3E(3E180)+3)  H(H(H(59)-1))
 seventillion  zakillion  1E(3E(3E210)+3)  H(H(H(69)-1))
 eightillion  yokillion  1E(3E(3E240)+3)  H(H(H(79)-1))
 nintillion  nekillion  1E(3E(3E270)+3)  H(H(H(89)-1))
 hundrillion  hotillion 1E(3E(3E300)+3)
 H(H(H(99)-1))
 - botillion
1E(3E(3E600)+3)
 H(H(H(199)-1))
 -  trotillion  1E(3E(3E900)+3)  H(H(H(299)-1))
 -  totillion  1E(3E(3E1200)+3)  H(H(H(399)-1))
 -  potillion  1E(3E(3E1500)+3)  H(H(H(499)-1))
 -  exotillion  1E(3E(3E1800)+3)  H(H(H(599)-1))
 -  zotillion  1E(3E(3E2100)+3)  H(H(H(699)-1))
 -  yootillion  1E(3E(3E2400)+3)  H(H(H(799)-1))
 -  notillion  1E(3E(3E2700)+3)  H(H(H(899)-1))
 thousillion kalillion
 1E(3E(3E3000)+3)  H(H(H(999)-1))
-
dalillion
1E(3E(3E6000)+3)
 H(H(H(1999)-1))
 -  tralillion  1E(3E(3E9000)+3)  H(H(H(2999)-1))
 -  talillion  1E(3E(3E12,000)+3)  H(H(H(3999)-1))
 -  palillion  1E(3E(3E15,000)+3)  H(H(H(4999)-1))
 -  exalillion  1E(3E(3E18,000)+3)  H(H(H(5999)-1))
 -  zalillion  1E(3E(3E21,000)+3)  H(H(H(6999)-1))
 -  yalillion  1E(3E(3E24,000)+3)  H(H(H(7999)-1))
 -  nalillion  1E(3E(3E27,000)+3)  H(H(H(8999)-1))
 -  dakalillion  1E(3E(3E30,000)+3)  H(H(H(9999)-1))
 -  hotalillion  1E(3E(3E300,000)+3)  H(H(H(99,999)-1))
 -  mejillion  1E(3E(3E3,000,000)+3)  H(H(H(999,999)-1))
 -  dakejillion  1E(3E(3E30,000,000)+3)  H(H(H(9,999,999)-1))
 -  hotejillion 1E(3E(3E300,000,000)+3)
H(H(H(99,999,999)-1))
 -  gijillion  1E(3E(3E3,000,000,000)+3)  H(H(H(999,999,999)-1))
 -  astillion  1E(3E(3E3,000,000,000,000)+3)  H(H(H(H(3)-1)-1))
 -  lunillion 1E(3E(3E3,000,000,000,000,000)+3)
 H(H(H(H(4)-1)-1))
 -  fermillion  1E(3E(3E3,000,000,000,000,000,000)+3)  H(H(H(H(5)-1)-1))
 -  jovillion  1E(3E(3E(3E21))+3)  H(H(H(H(6)-1)-1))
 -  solillion 1E(3E(3E(3E24))+3)
H(H(H(H(7)-1)-1))
 -  betillion  1E(3E(3E(3E27))+3)  H(H(H(H(8)-1)-1))
 -  glocillion  1E(3E(3E(3E30))+3)  H(H(H(H(9)-1)-1))
 -  gaxillion  1E(3E(3E(3E33))+3)  H(H(H(H(10)-1)-1))
 -  supillion  1E(3E(3E(3E36))+3)  H(H(H(H(11)-1)-1))
 -  versillion  1E(3E(3E(3E39))+3)  H(H(H(H(12)-1)-1))
 -  multillion  1E(3E(3E(3E42))+3)  H(H(H(H(13)-1)-1))

    In addition to these, Bowers also includes members of the googol series for size comparison, and also includes some erroneous illions from other systems, presumably to show that his system surpasses other popular illion names such as the bentrizillion.

    The following table is a complete list of names appearing in both of Bowers lists which are not strictly meant as part of his system. For convenience they are also listed in size order from least to greatest:

Miscellaneous Names on Bowers' Lists

 Name Scientific Notation
 googol 1E100
 platillion 1E6000
 googolplex 1E(1E100)
googolduplex
1E(1E(1E100))
manillion
1E(3E(3E30,000)+3)
 lakhillion  1E(3E(3E300,000)+3)
 crorillion  1E(3E(3E30,000,000)+3)
 awkillion  1E(3E(3E300,000,000)+3)
 googoltriplex 1E(1E(1E(1E100)))
bentrizillion*
1E(6E(6E(6E6,000,000,000)))
googolquadraplex
1E(1E(1E(1E(1E100))))
 googolquinplex 1E(1E(1E(1E(1E(1E100)))))

* On Bowers list a bentrizillion is defined as 10^(6*10^(6*10^(6*10^6billion))). It is uncertain whether a billions means 1E9 or 1E12 here.

    We'll learn more about the googol series in the next chapter. For some reason no real information seems to exist on the bentrizillion and platillion other than Bowers website and people quoting his website. Bowers himself admits to not knowing where they came from. It is clear however from the definitions that these names must have been coined within a long scale system.

    The terms manillion, lakhillion, crorillion, and awkillion do not name unique numbers. Instead they are alternative names for numbers in Bowers newer system. One telling thing about these names is that they occur just after a thousillion. This implies that someone must have seen Bowers list, coined a few extra after a thousillion, and these somehow managed to spread to the point where they got Bowers notice. Perhaps they spurred him on to create his new names.

    Excluding these names Bowers new list includes 139 milestone -illions. If we subtract out the 39 names under a millillion, we find that Bowers coined 100 illions exactly!

    This number however would pale in comparison to the number of illions that would exist if every gap in his system was filled up to a multillion.

    Let's now take a closer look at how intermediate terms might be formed:

Deeper Analysis : Filling in the Gaps in Bowers List

    We will now begin to take a closer look at Bowers system. Of prime importance to us here is how to construct all of the intermediate names between Bowers milestone illions. Unfortunately we can not simply list out all the possible names because the number of them would be so staggeringly huge that it could not fit within the known universe. This is not an exaggeration, its an understatement! To prove this consider the following:

    If our largest illion has the value H(n), then we must have "n" -illions in order to have a complete system up to H(n). In Bowers case a multillion is the largest illion. It is equal to H(H(H(H(13)-1)-1)) in half-scale notation. Removing an H-function we find that this implies n = H(H(H(13)-1)-1) = H(H(1E42-1)-1) = H(1E(3E42)-1) = 1E(3E(3E42)). That's a 1 followed by 3*10^(3*10^42) zeroes. Compare this to the number of sub-atomic particles in the known universe which is a mere 1E80, or 1 followed by 80 zeroes. Basically even the number of illion names has a hyper-exponential number of digits! There is no hope of listing out all of the intermediates one by one!

    Therefore, in order to describe how to construct all of the intermediates we will need to develop a set of rules of construction. This is what the remainder of the article will be about.

Terminology: Tiers and roots

    Before we begin I'd like to define what I mean by a "tier" in relation to a general power-based illion series, because we will be using this concept throughout the rest of this article.

    A tier is essentially a group of roots used to describe a certain set of names. What is a "root"? A root is either a prefix or a suffix. Essentially a root is a part of a word. Roots can be combined in sequence in order to form words. This practice is most common in naming numbers, however roots play a part even in ordinary language. For example the word "abnormal", is formed from the roots "ab" for "not", and "normal". The definition then follows from the combination of these meanings as "not normal". In a similar way, "numeric roots" can be combined to form number names. For example the number "twenty four" is the combination of the root "Twenty" and the root "Four". Their combined meaning is the sum of the value of the roots. All of the illion series we've been considering can essentially be broken down into complex "root systems". A root system is a set of rules for how roots can be combined and how to interpret them. Roots systems are advantageous because we don't have to remember millions of names in order to construct them all. We only need to remember a handful of roots that can be combined in various ways to form any name within the scope of the system.

    We can further break down roots in to various classes each with a different function:

    Numeric roots such as the numbers 1~20 are what we might call additive roots. These roots have a specific meaning and when combining the numeric values are simply added together. Another important numeric root type are multiplicative roots. An example is the root "hundred". When it is combined with the root "two" to form "two hundred", the roots are not added to obtain 102. Instead they are multiplied together to obtain 200. Interestingly if the order is reversed to "hundred two" the implied meaning is 102. Multiplicative roots therefore have an important property: order matters. Generally in almost all languages when a smaller numeric root is followed by a larger multiplicative root, they are to be multiplied together. When the smaller roots follows after the multiplicative root it is to be added.

    A third kind of root we can call separatrix roots, or separatrices for short. They operate in a similar manner to multiplicative roots but are much more general. A multiplicative root can only be multiplied by the first root to its left. However a separatrix is multiplied by the result of a "group" of roots to its left. A group here refers to a set of legal combinations of roots. These roots may be of any type. The separatrix must be defined to include what kind of groups it will allow. An example of a separatrix is the numeric root "thousand". A thousand can act as a multiplicative root as in "three thousand" but it can also act as a separatrix when it is multiplied not by a single root but by a group as in "two hundred seven thousand".

    The last kinds of root we will be considering we can call modifiable roots, or mods for short. A modifiable root, or mod becomes augmented by a "modifier group" to augment its own meaning. A mod/modifier group combo can be used to form a separatrix. For example the separatrix, "quintillion" is formed from the modifiable root "illion" combined with its modifier "quint" which is latin for 5. The meaning is therefore the 5th member of the illion series.

    We now have sufficient terminology to describe what a tier is properly:

    A tier represents all of the constructions that can be formed using a set number of separatrix classes, that can't be described using constructions with one less separatrix class.

    A separatrix class can be any positive integer and represents the rank of the separatrix. The higher the number the higher the rank. A class 1 separatrix separates ordinary groups. A class 2 separatrix separates modifier groups within a class 1 separatrix. A class 3 separatrix separates modifier groups within a class 2 separatrix ... and so on.

    So a tier is basically the measure of the highest separator class allowed. To give you a better understanding of what we're talking about I'll describe the first few tiers.

    Let's begin with "tier 0" constructions:

    Tier 0
constructions contain no separatrices what so ever. This means that tier 0 only includes numbers from 1 to 999. "one thousand" requires the use of the separatrix "thousand", so this number can not be included in tier 0, nor any higher number.

    Tier 1 allows the use of only class 1 separatrices. This means the class 1 separatrix can only use additive and multiplicative roots as modifiers. A class 1 separatrix can not contain any separatrices within its modifier group. Allowable separatrices in Tier 1 include, a thousand, million, billion, trillion, ... all of the standard illions up to a centillion, all the way up to the 999th illion. Tier 1 ends not at H(999) but at H(1000)-1. In other words, the largest tier 1 number is one less than the smallest tier 2 number.

    Tier 2 allows the use of class 2 separatrices. These act as separators within the modifier group of class 1 separatrices. The smallest tier 2 number would be the 1000th illion, called a millillion in Bowers nomenclature. Here "milli" is a modifier for the mod root "illion". Numbers such as micrillion, nanillion, picillion, femtillion, attillion, etc. are all example of tier 2 numbers. Tier 2 ends at a killillion-1, or the number just before the smallest tier 3 number.

    Tier 3 allows use of class 3 separatrices. In the case of Bowers system it begins with a killillion and ends with a kalillion-1.

    Tier 4 allows use of class 4 separatrices. In Bowers system tier 4 begins with a kalillion (formally a thousillion). Bowers system does not completely fill out tier 4, and ends somewhere within it. We can therefore classify Bowers system as a "4 tiered illion series".

    Keep in mind that the boundary points between tiers depends on the system of separatrices used. For example, there are actually 1000 class 1 separators in Bowers system, not 999 because besides the 999 legal class 1 illions, we must also recognize that a thousand is also a class 1 separatrix. This is not always the case. In Russ Rowletts greek based system, for example, there are exactly 999 class 1 separatrices, because the greek modifier prefixes represent the power of a thousand. This means that the smallest tier 2 number in Russ Rowletts system would be 1E3000, while the smallest in Bowers would be 1E3003. Depending on how we define things we might even say that the smallest tier 2 long scale number would be 1E6000. For this reason, understand that the boundaries are dependent upon the system considered.

    We will now go over each tier of Bowers system, one by one, in much greater detail, to develop a complete system for describing any Bowers' Style illion.

The 0th Tier Intermediates

    Since Bowers is extending the standard American number names, his Tier 0 numbers are simply the ordinary english names from 1 to 999.
Although forming these numbers should be elementary we will quickly be going over the mechanics of them to elucidate the basic principles we will be using at all of the higher tiers. To form the first 999 numbers we actually need only 24 roots. These are:

    one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thir, fif, teen, twenty, thirty, forty, fifty, sixty seventy,eighty, ninety, hundred

    The following table includes all tier 0 roots:

Tier 0 Roots

 Value Ones
Tens
Hundreds
 1 one/eleven
ten/teen
hundred
 2  two/twelve twenty
 -
 3  three/thir  thirty  -
 4  four  forty  -
 5  five/fif fifty
 -
 6  six  sixty  -
 7  seven  seventy  -
 8  eigh(t)  eighty  -
 9  nine  ninety  -

    The above table is what we can call a root table. It is different from a list of numbers, and instead provides us with the "components" to construct numbers. This will be our primary way of making sense of Bowers system, without having to list every single name that can be constructed within his system.

    The basic principles of a root table is that it should include all the necessary combinations of letters (roots) that are needed to construct any number within a given range. Special rules can be included to deal with nuances. Roots that are part of a "tier group" can be broken up into ones, tens and hundreds. Under these columns roots can take any value from 1 to 9. A roots base value is dependent on where its located on the table. For example, if the root is in the tens column in row 5, then its value is 50. Normally there should be at least one unique root for every position on the table. These roots are usually of the additive type, and can be listed either in decreasing or increasing order. For english we list the roots in decreasing order.

    One special feature of english, which breaks slightly from what is described above, is that we don't have unique names for 200, 300, 400, etc. as we do for 20,30,40 etc. Instead "hundred" acts as a multiplicative root, and must be combined with a ones root to its left to give it a definite value.

    You may notice in the above table the use of the slash, " / ". This means that there is more than one root to chose from within a particular position. Which is used depends on the situation and the rules. The roots, listed from left to right, are referred to as the 1st option, 2nd option, etc.

    The parentheses , " ( ) " , contain "optional" letters. These can either be dropped or added based on the situation and the rules. Sometimes commas may be used to separate letters within the parentheses. This simply means that there is more than one optional letter to be added.

    The above table of roots can be used to construct any number from 1 to 999 by following these rules:

1. If hundreds & tens = 0 , use 1st option ones roots, with all optional letters included to represent the number.

2. If hundreds = 0 & tens = 1, use "ten" if ones = 0. If ones = 1 or 2 , use 2nd option ones root, without any tens root. Otherwise use 2nd option ones root with all optional letters removed followed by 2nd option tens root (teen).

3. If hundreds = 0 & tens > 1, use tens root followed by 1st option ones root with all optional letters included.

4. If hundreds > 0 & tens = 0, use 1st option ones root (optional letters included) equal to value of hundreds followed by root "hundred". Follow this by 1st option ones root equal to value of ones.

5. If hundreds > 0 & tens = 1, use 1st option ones root (optional letters included) equal to value of hundreds followed by root "hundred". Follow this with "ten" if ones = 0, with "eleven" if ones = 1, with "twelve" if ones = 2; otherwise follow with 2nd option ones roots with optional letters removed followed by "teen".

6. If hundreds > 0 & tens > 0, use 1st option ones root (optional letters included) equal to vlaue of hundreds followed by root "hundred". Follow with appropriate tens root and finish with 1st option ones root with optional letters included.


    These rules should in theory be all that is necessary to explain the mechanical construction of naming numbers from 1 to 999. Note that this particular naming scheme makes no use of "and".

    The following table shows the names of the numbers using the above scheme. You might want to compare it to the above rules to get a feel for how this works:

List of Tier 0 Numbers (1-999)

 Name Number (Decimal)
 one 1
 two  2
 three  3
 four  4
 five  5
 six  6
 seven  7
 eight  8
 nine  9
 ten  10
 eleven  11
 twelve  12
 thirteen  13
 fourteen  14
 fifteen  15
 sixteen  16
 seventeen  17
 eighteen  18
 nineteen  19
 twenty  20
 twenty one
 21
 twenty two
 22
 twenty three
 23
 twenty four
 24
 twenty five
 25
 twenty six
 26
 twenty seven
 27
 twenty eight
 28
 twenty nine
 29
 thirty  30
 thirty one
 31
 thirty two
 32
 thirty three
 33
 thirty four
 34
 ...  ...
 forty  40
 forty one
 41
 forty two
 42
 forty three
 43
 ...  ...
 fifty  50
 fifty one
 51
 fifty two
 52
 ...  ...
 sixty  60
 sixty one
 61
 ...  ...
 seventy  70
 ...  ...
 eighty  80
 ...  ...
 ninety  90
 ...  ...
 ninety nine
 99
 one hundred
 100
 one hundred one
 101
 one hundred two
 102
 one hundred three
 103
 one hundred four
 104
 ...  ...
 one hundred ten
 110
 one hundred eleven
 111
 one hundred twelve
 112
 one hundred thirteen
 113
 one hundred fourteen
 114
 one hundred fifteen
 115
 one hundred sixteen
 116
 one hundred seventeen
 117
 one hundred eighteen
 118
 one hundred nineteen
 119
 one hundred twenty
 120
 one hundred twenty one
 121
 one hundred twenty two
 122
 one hundred twenty three
 123
 one hundred twenty four
 124
 ...  ...
 one hundred thirty
 130
 ...  ...
 one hundred forty
 140
 ...  ...
 one hundred fifty
 150
 ...  ...
 ...
 ...
 one hundred ninety nine
 199
 two hundred
 200
 two hundred one
 201
 two hundred two
 202
 ...  ...
 two hundred ten
 210
 two hundred eleven
 211
 two hundred twelve
 212
 two hundred thirteen
 213
 ...  ...
 two hundred twenty
 220
 ...  ...
 two hundred thirty
 230
 ...  ...
 ...  ...
 two hundred ninety nine
 299
 three hundred
 300
 three hundred one
 301
 ...  ...
 three hundred ten
 310
 three hundred eleven
 311
 three hundred twelve
 312
three hundred thirteen
 313
 ...  ...
 three hundred twenty
 320
 ... ...
 three hundred thirty
 330
 ...  ...
 ...  ...
 three hundred ninety nine
 399
 four hundred
 400
 four hundred one
 401
 ...  ...
 four hundred ten
 410
 four hundred eleven
 411
 four hundred twelve
 412
 four hundred thirteen
 413
 ...  ...
 four hundred twenty
 420
 ...  ...
 four hundred thirty
 430
 ...  ...
 ...  ...
 four hundred ninety nine
 499
 five hundred
 500
 five hundred one
 501
 ...  ...
 five hundred ten 510 
 ...  ...
 five hundred twenty  520
 ...  ...
 ...  ...
 five hundred ninety nine  599
 six hundred  600
 six hundred one  601
 ...  ...
 six hundred ten  610
 ...  ...
 six hundred twenty  620
 ...  ...
 ...  ...
 six hundred ninety nine  699
 seven hundred  700
 seven hundred one  701
 ...  ...
 seven hundred ten  710
 ...  ...
 seven hundred twenty  720
 ...  ...
 ...  ...
 seven hundred ninety nine  799
 eight hundred  800
 eight hundred one  801
 ...  ...
 eight hundred ten  810
 ...  ...
 eight hundred twenty  820
 ...  ...
 ...  ...
 eight hundred ninety nine  899
 nine hundred  900
 nine hundred one  901
 nine hundred two  902 
 nine hundred three 903 
 ...  ...
 nine hundred nine  909
 nine hundred ten  910
 nine hundred eleven  911
 nine hundred twelve  912
 nine hundred thirteen  913
 ...  ...
 nine hundred nineteen  919
 nine hundred twenty  920
 nine hundred twenty one  921
 nine hundred twenty two  922
 nine hundred twenty three  923
 ...  ...
 nine hundred twenty nine  929
 nine hundred thirty  930
 nine hundred thirty one  931
 nine hundred thirty two  932
 ...  ...
 nine hundred thirty nine  939
 nine hundred forty  940
 nine hundred forty one  941
 ...  ...
 nine hundred fifty  950
 ...  ...
 nine hundred sixty  960
 ...  ...
 nine hundred seventy  970
 ...  ...
 nine hundred eighty  980
 ...  ...
 nine hundred eighty nine  989
 nine hundred ninety  990
 nine hundred ninety one  991
 ...  ...
 nine hundred ninety seven  997
 nine hundred ninety eight  998
 nine hundred ninety nine  999

    Hopefully this will familiarize you with the basic way we be using root tables. For each Tier we will require a new root table and a new set of rules for working with them. Let's now move on to Tier 1:

The 1st Tier Intermediates

    We now introduce the use of separators, or separatrices. After "nine hundred ninety nine" of coarse comes "one thousand". The root "thousand" here is acting as a separator between the "ones group" and the "thousands group". A group here refers to any 0th Tier construction. Let any 0th Tier construction be symbolized by G(k) where G(k) is the kth group corresponding to an english name for any number from 1 to 999. If G = 0, then we use a "blank space" which means we use no roots. Basically using the separatrix "thousand" we can form names of the form :
 
G(1) thousand G(0)
 
where this is equivalent to G(1)*1000+G(0)
 
    This of coarse allows us to name numbers up to 999,999. Note that class 1 Separatrices act just like commas in ordinary decimal notation except that a rank is also associated with them. To go further we simply need more class 1 separatrices. In sequence, some separatrices after a thousand are "million", "billion", "trillion", "quadrillion", "quintillion", etc. For each of these, a 0th tier group can occur before it as a "group multiplier". For example "nine hundred ninety nine million" is 999*1,000,000.
 
    Say we have Separatrices marked H(0), H(1), ... and the way to H(n). We can therefore say every number which can be named with these separatrices can be written in the form:
 
G(n+1) H(n) G(n) H(n-1) ... ... G(2) H(1) G(1) H(0) G(0)

where this is equivalent to:

G(n+1)*H(n) + G(n)*H(n-1) + ... ... + G(2)*H(1) + G(1)*H(0) + G(0)

 
    If any kth group, G(k), where k > 0 is equal to zero, G(k) and H(k-1) must be removed from the above construction. If G(0) = 0 then G(0) = " "

    As an example consider the number 384,104,000,792,234. Here we have G(4) = 384, G(3) = 104, G(2) = 0, G(1) = 792, and G(0) = 234. Since the highest group is G(4), the highest separator we will need will be H(3). Thus we have:

384*H(3) + 104*H(2) + 0*H(1) + 792*H(0) + 234

    We must drop 0*H(1), and by substituting the appropriate "groups" and "separators" we obtain the canonical name:

three hundred eighty four trillion one hundred four billion
seven hundred ninety two
thousand two hundred thirty four

    Here is another example. Consider the number 120,406,089,000. Here we have G(3) = 120, G(2) = 406, G(1) = 89, and G(0) = 0. The highest separator we need is H(2). Thus we have:

120*H(2) + 406*H(1) + 89*H(0) + 0

    We must drop G(0) since G(0) = 0, and leave the last group blank. Substituting in the appropriate groups and separators we obtain the canonical name:

one hundred twenty billion four hundred six million eighty nine thousand

    As you can see all we need to continue into tier 1 territory is a series of separators. What separators does Bowers use? Generally speaking he uses the canonical illions, and Conway & Guys system, although his usage is not identical.

    On Bowers web page listing his milestone illions he states that rules for naming numbers up to a millillion are mentioned in "The Book of Numbers" by Conway and Guy. It is clear from this statement that Bowers intends to take Conway and Guy's system up to the 999th illion as canonical. However, there are some subtle differences between Bowers nomenclature and the Conway&Guy nomenclature. For example Bowers lists the 12th illion as "doedecillion", while Conway&Guy use the more standard "duodecillion". Bowers uses the more standard "sexdecillion" for the 16th illion, while Conway&Guy recommend "sedecillion" as closer to true latin. While Conway&Guys system are designed to list the modifiers (1st tier roots) from ones tens to hundreds, its unclear what order Bowers has in mind from his milestone examples. Particularly erroneous is his suggested sequence of "cenuntillion", "duocentillion", and "centretillion" for the 101st, 102nd, and 103rd illion respectively. To avoid a lot of confusion, I'll assume that these are special cases, and that under all other circumstances the order follows that of Conway&Guy. With these nuances in mind, here is a table of 1st tier roots for Bowers' system:

Bowers' Tier 1 Roots

 Value 1st
Ones root
1st
Tens root
1st
Hundreds root
 1
 m/un(t) dec(i)
cen(t)
 2  b/doe/duo  vigint(i)  ducen(t)
 3  tr/tre(t)  trigint(i)  trecen(t)
 4  quadr/quattuor  quadragint(i)  quadringen(t)
 5  quint/quin  quinquagint(i)  quingen(t)
 6  sext/sex  sexagint(i)  sescen(t)
 7  sept/septen  septuagint(i)  septingen(t)
 8  oct/octo  octogint(i)  octingen(t)
 9  non/novem  nonagint(i)  nongen(t)

    Here we have 37 tier 1 roots. Letters within parenthesis may be dropped or added according to the rules. Here are the basic rules of combining these roots to form a modifier for the mod root "illion"

1. If all ones, tens and hundreds value = 0, use "thousand" as a tier 1 separatrix.

2. If tens and hundreds value = 0, use first option ones roots followed by illion to form the tier 1 separatrix.

3. If tens value > 0 , and hundreds value = 0, list roots from ones to tens, and use 2nd option ones roots (drop any " t "), and drop " i " from tens root before following with illion to form the tier 1 separatrix.

4. If hundreds value > 0, and tens value = 0, drop " t " from hundreds root, if ones root = 1 or 3, and  list 2nd option ones root after the hundreds root with its " t " included. Follow with illion to form the tier 1 separatrix.

5.
If hundreds value > 0, tens value = 0 and the ones
root = 2 then use its 3rd option and place it to the left of the hundreds root with " t " included followed by illion to form the tier 1 separatrix. Otherwise use 2nd option ones roots followed by hundreds roots with " t " included to form the tier 1 separatrix.

6. If tens and hundreds > 0, list roots from ones tens to hundreds, and use 2nd option ones             roots (with t dropped). Don't drop " i " from tens root, before following with hundreds root with " t " included followed by illion to form the tier 1 separatrix.


    The rules above can be used to name any separator H(n), where n indicates the number. For example:

    H(513) would be separator 513. Since the hundreds place > 0 only rules 4,5, or 6 can apply. Since tens > 0 only rule 6 applies (note: only one rule can apply to any given separator). Rule 6 says list 2nd option ones root with t dropped, since ones = 3, we use the root "tre(t)" where the " t " is dropped. This is followed by the tens root "dec(i)" with the " i " included, and the hundreds root "quingen(t)" with the " t " included followed by illion. This forms:

tre - deci - quingent - illion

officially we write:

tredeciquingentillion

    These rules may seem a little involved. Just to make sure this is made clear here is a table containing some class 1 separators:

List of Bowers' Style Class 1 Separators

 Bowers'
Class 1 Separators
 Scientific E Notation
 Half-Scale Notation
 thousand  1E3 H(0)
 million  1E6
H(1)
 billion  1E9 H(2)
 trillion  1E12  H(3)
 quadrillion  1E15 H(4)
 quintillion  1E18  H(5)
 sextillion  1E21  H(6)
 septillion  1E24  H(7)
 octillion  1E27  H(8)
 nonillion  1E30  H(9)
 decillion  1E33  H(10)
 undecillion  1E36  H(11)
 doedecillion  1E39  H(12)
 tredecillion  1E42  H(13)
 quattuordecillion  1E45  H(14)
 quindecillion  1E48  H(15)
 sexdecillion  1E51  H(16)
 septendecillion  1E54  H(17)
 octodecillion  1E57  H(18)
novemdecillion
 1E60  H(19)
 vigintillion  1E63 H(20)
 unvigintillion  1E66  H(21)
 doevigintillion  1E69  H(22)
 trevigintillion  1E72  H(23)
 quattuorvigintillion  1E75  H(24)
 quinvigintillion  1E78  H(25)
 sexvigintillion  1E81  H(26)
 septenvigintillion  1E84  H(27)
 octovigintillion  1E87  H(28)
 novemvigintillion  1E90  H(29)
 trigintillion  1E93  H(30)
 untrigintillion  1E96  H(31)
 doetrigintillion  1E99  H(32)
 tretrigintillion  1E102  H(33)
 quattuortrigintillion  1E105  H(34)
 quintrigintillion  1E108  H(35)
 sextrigintillion  1E111  H(36)
 septentrigintillion  1E114  H(37)
 octotrigintillion  1E117  H(38)
 novemtrigintillion  1E120  H(39)
quadragintillion
 1E123  H(40)
 unquadragintillion  1E126  H(41)
 doequadragintillion  1E129  H(42)
 trequadragintillion  1E132  H(43)
 quattuorquadragintillion  1E135  H(44)
 ...  ...  ...
 novemquadragintillion  1E150  H(49)
 quinquagintillion  1E153  H(50)
 unquinquagintillion  1E156  H(51)
 doequinquagintillion  1E159  H(52)
 trequinquagintillion  1E162  H(53)
 ...  ...  ...
 novemquinquagintillion  1E180  H(59)
 sexagintillion  1E183  H(60)
 unsexagintillion  1E186  H(61)
 doesexagintillion  1E189  H(62)
 ...  ...  ...
 novemsexagintillion  1E210  H(69)
 septuagintillion  1E213  H(70)
 unseptuagintillion  1E216  H(71)
 ...  ...  ...
 novemseptuagintillion  1E240  H(79)
 octogintillion  1E243  H(80)
 unoctogintillion  1E246  H(81)
 ...  ...  ...
 octooctogintillion  1E267  H(88)
 novemoctogintillion  1E270  H(89)
 nonagintillion  1E273  H(90)
 unnonagintillion  1E276  H(91)
 ...  ...  ...
 novemnonagintillion  1E300  H(99)
 centillion 1E303
H(100)
 cenuntillion 1E306
H(101)
 duocentillion 1E309
H(102)
 centretillion 1E312
H(103)
 quattuorcentillion 1E315
H(104)
 quincentillion  1E318  H(105)
 sexcentillion  1E321  H(106)
 septencentillion  1E324  H(107)
 octocentillion  1E327  H(108)
 novemcentillion  1E330  H(109)
 decicentillion  1E333  H(110)
 undecicentillion  1E336  H(111)
 doedecicentillion  1E339  H(112)
 tredecicentillion  1E342  H(113)
 quattuordecicentillion  1E345  H(114)
 ...  ...  ...
 novemdecicentillion  1E360  H(119)
 viginticentillion  1E363  H(120)
 unviginticentillion  1E366  H(121)
 doeviginticentillion  1E369  H(122)
 treviginticentillion  1E372  H(123)
 ...  ...  ...
 novemviginticentillion  1E390  H(129)
 triginticentillion  1E393  H(130)
 untriginticentillion  1E396  H(131)
 doetriginticentillion  1E399  H(132)
 ...  ...  ...
 novemtriginticentillion  1E420
 H(139)
 quadraginticentillion  1E423  H(140)
 unquadraginticentillion  1E426  H(141)
 ...  ...  ...
 novemquadraginticentillion  1E450  H(149)
 quinquaginticentillion  1E453  H(150)
 unquinquaginticentillion  1E456  H(151)
 ...  ...  ...
 novemquinquaginticentillion  1E480
 H(159)
 sexaginticentillion  1E483  H(160)
 unsexaginticentillion  1E486  H(161)
 ...
 ...  ...
 novemsexaginticentillion  1E510  H(169)
 septuaginticentillion  1E513  H(170)
 unseptuaginticentillion  1E516  H(171)
 ...  ...  ...
 novemseptuaginticentillion  1E540  H(179)
 octoginticentillion  1E543  H(180)
 unoctoginticentillion  1E546  H(181)
 ...  ...  ...
 novemoctoginticentillion  1E570  H(189)
 nonaginticentillion  1E573  H(190)
 unnonaginticentillion  1E576  H(191)
 ...  ...  ...
 novemnonaginticentillion  1E600  H(199)
 ducentillion  1E603  H(200)
 ducenuntillion  1E606  H(201)
 duoducentillion  1E609  H(202)
 ducentretillion  1E612  H(203)
 quattuorducentillion  1E615  H(204)
 quinducentillion  1E618  H(205)
 sexducentillion  1E621  H(206)
 septenducentillion  1E624  H(207)
 octoducentillion  1E627  H(208)
 novemducentillion  1E630  H(209)
 deciducentillion  1E633  H(210)
 undeciducentillion  1E636  H(211)
 doedeciducentillion  1E639  H(212)
tredeciducentillion
 1E642  H(213)
 ...  ...  ...
 novemdeciducentillion  1E660  H(219)
 vigintiducentillion  1E663  H(220)
 unvigintiducentillion  1E666  H(221)
 doevigintiducentillion  1E669  H(222)
 ...  ...  ...
 trigintiducentillion  1E693  H(230)
 ...  ...  ...
 quadragintiducentillion  1E723  H(240)
 ...  ... ...
 quinquagintiducentillion  1E753  H(250)
 ...  ...  ...
 sexagintiducentillion  1E783  H(260)
 ...  ...  ...
 septuagintiducentillion  1E813  H(270)
 ...  ...  ...
 octogintiducentillion  1E843  H(280)
 ...  ...  ...
 nonagintiducentillion  1E873  H(290)
 ...  ...  ...
 novemnonagintiducentillion  1E900  H(299)
 trecentillion  1E903  H(300)
trecenuntillion
 1E906  H(301)
 duotrecentillion  1E909  H(302)
 trecentretillion  1E912  H(303)
 quattuortrecentillion  1E915  H(304)
 quintrecentillion  1E918  H(305)
 ...  ...  ...
 novemtrecentillion  1E930  H(309)
 decitrecentillion  1E933  H(310)
 undecitrecentillion  1E936  H(311)
 doedecitrecentillion  1E939  H(312)
 tredecitrecentillion  1E942  H(313)
 ...  ...  ...
 novemdecitrecentillion  1E960  H(319)
 vigintitrecentillion  1E963  H(320)
 unvigintitrecentillion  1E966  H(321)
 doevigintitrecentillion  1E969  H(322)
 ...  ...  ...
 trigintitrecentillion  1E993  H(330)
 ...  ...  ...
 quadragintitrecentillion  1E1023  H(340)
 ...  ...  ...
 quinquagintitrecentillion  1E1053  H(350)
 ...  ...  ...
 sexagintitrecentillion  1E1083  H(360)
 ...  ...  ...
 septuagintitrecentillion  1E1113  H(370)
 ...  ...  ...
 octogintitrecentillion  1E1143  H(380)
 ...  ...  ...
 nonagintitrecentillion  1E1173  H(390)
 ...  ...  ...
 novemnonagintitrecentillion  1E1200  H(399)
 quadringentillion  1E1203  H(400)
 quadringenuntillion  1E1206  H(401)
 duoquadringentillion  1E1209  H(402)
 quadringentretillion  1E1212  H(403)
quattuorquadringentillion
 1E1215  H(404)
 ...  ... ...
 novemquadringentillion  1E1230  H(409)
 deciquadringentillion  1E1233  H(410)
 undeciquadringentillion  1E1236  H(411)
 doedeciquadringentillion  1E1239  H(412)
 ...  ...  ...
 vigintiquadringentillion  1E1263  H(420)
 ...  ...  ...
 trigintiquadringentillion  1E1293  H(430)
 ...  ...  ...
 quadragintiquadringentillion  1E1323  H(440)
 ...  ...  ...
 quinquagintiquadringentillion  1E1353  H(450)
 ...  ...  ...
 sexagintiquadringentillion  1E1383  H(460)
 ...  ...  ...
 septuagintiquadringentillion  1E1413  H(470)
 ...  ...  ...
 octogintiquadringentillion  1E1443  H(480)
 ...  ...  ...
 nonagintiquadringentillion  1E1473  H(490)
 ...  ...  ...
 novemnonagintiquadringentillion  1E1500  H(499)
 quingentillion  1E1503 H(500)
 quingenuntillion  1E1506  H(501)
 duoquingentillion  1E1509  H(502)
 quingentretillion  1E1512  H(503)
 ...  ...  ...
 deciquingentillion  1E1533  H(510)
 undeciquingentillion  1E1536  H(511)
 doedeciquingentillion  1E1539  H(512)
 ...  ...  ...
 vigintiquingentillion  1E1563  H(520)
 ...  ...  ...
 trigintiquingentillion  1E1593  H(530)
 ...  ...  ...
 quadragintiquingentillion  1E1623  H(540)
 ...  ...  ...
 quinquagintiquingentillion  1E1653  H(550)
 ...  ...  ...
 sexagintiquingentillion  1E1683  H(560)
 ...  ...  ...
 septuagintiquingentillion  1E1713  H(570)
 ...  ...  ...
 octogintiquingentillion  1E1743  H(580)
 ...  ...  ...
 nonagintiquingentillion  1E1773  H(590)
 ...  ...  ...
 novemnonagintiquingentillion  1E1800  H(599)
 sescentillion  1E1803  H(600)
 sescenuntillion  1E1806  H(601)
 duosescentillion  1E1809  H(602)
 sescentretillion  1E1812  H(603)
 ...  ...  ...
 decisescentillion  1E1833  H(610)
 undecisescentillion  1E1836  H(611)
 doedecisescentillion  1E1839  H(612)
 ...  ...  ...
 vigintisescentillion  1E1863  H(620)
 ...  ...  ...
 trigintisescentillion  1E1893  H(630)
 ...  ...  ...
 quadragintisescentillion  1E1923  H(640)
 ...  ...  ...
 quinquagintisescentillion  1E1953  H(650)
 ...  ...  ...
 sexagintisescentillion  1E1983  H(660)
 ...  ...  ...
 septuagintisescentillion  1E2013  H(670)
 ...  ...  ...
 octogintisescentillion  1E2043  H(680)
 ...  ...  ...
 nonagintisescentillion  1E2073  H(690)
 ...  ...  ...
 novemnonagintisescentillion  1E2100  H(699)
 septingentillion  1E2103  H(700)
 septingenuntillion  1E2106  H(701)
 duoseptingentillion  1E2109  H(702)
 septingentretillion  1E2112  H(703)
 ...  ...  ...
 deciseptingentillion  1E2133  H(710)
 undeciseptingentillion  1E2136  H(711)
 doedeciseptingentillion  1E2139  H(712)
 ...  ...  ...
 vigintiseptingentillion  1E2163  H(720)
 ...  ...  ...
 trigintiseptingentillion  1E2193  H(730)
 ...  ...  ...
 quadragintiseptingentillion  1E2223  H(740)
 ...  ...  ...
 quinquagintiseptingentillion  1E2253  H(750)
 ...  ...  ...
 sexagintiseptingentillion  1E2283  H(760)
 ...  ...  ...
 septuagintiseptingentillion  1E2313  H(770)
 ...  ...  ...
 octogintiseptingentillion  1E2343  H(780)
 ...  ...  ...
 nonagintiseptingentillion  1E2373  H(790)
 ...  ...  ...
 novemnonagintiseptingentillion  1E2400  H(799)
 octingentillion  1E2403  H(800)
 octingenuntillion  1E2406  H(801)
 duooctingentillion  1E2409  H(802)
 octingentretillion  1E2412  H(803)
 ...  ...  ...
 decioctingentillion  1E2433  H(810)
 undecioctingentillion  1E2436  H(811)
 doedecioctingentillion  1E2439  H(812)
 ...  ...  ...
 vigintioctingentillion  1E2463  H(820)
 ...  ...  ...
 trigintioctingentillion  1E2493  H(830)
 ...  ...  ...
 quadragintioctingentillion  1E2523  H(840)
 ...  ...  ...
 quinquagintioctingentillion  1E2553  H(850)
 ...  ...  ...
 sexagintioctingentillion  1E2583  H(860)
 ...  ...  ...
 septuagintioctingentillion  1E2613  H(870)
 ...  ...  ...
 octogintioctingentillion  1E2643  H(880)
 ...  ...  ...
 nonagintioctingentillion  1E2673  H(890)
 ...  ...  ...
 novemnonagintioctingentillion  1E2700  H(899)
 nongentillion
 1E2703  H(900)
 nongenuntillion  1E2706  H(901)
 duonongentillion  1E2709  H(902)
 nongentretillion  1E2712  H(903)
 quattuornongentillion  1E2715  H(904)
 ...  ...  ...
 novemnongentillion  1E2730  H(909)
 decinongentillion  1E2733  H(910)
 undecinongentillion  1E2736  H(911)
 doedecinongentillion  1E2739  H(912)
 ...  ...  ...
 vigintinongentillion  1E2763  H(920)
 ...  ...  ...
 trigintinongentillion  1E2793  H(930)
 ...  ...  ...
 quadragintinongentillion  1E2823  H(940)
 ...  ...  ...
 quinquagintinongentillion  1E2853  H(950)
 ...  ...  ...
 sexagintinongentillion  1E2883  H(960)
 ...  ...  ...
 septuagintinongentillion  1E2913  H(970)
 ...  ...  ...
 octogintinongentillion  1E2943  H(980)
 ...  ...  ...
 nonagintinongentillion  1E2973  H(990)
 ...  ...  ...
 novemnonagintinongentillion  1E3000  H(999)

     The largest number we can express at Tier 1 is not novemnonagintinongentillion. Instead it would be ...

nine hundred ninety nine novemnonagintinongentillion nine hundred ninety nine octononagintinongentillion nine hundred ninety nine septennonagintinongentillion

... ... ... ... ... ...

nine hundred ninety nine trillion nine hundred ninety nine billion nine hundred ninety nine million
nine hundred ninety nine thousand nine hundred ninety nine


    In other words, its the number generated by filling all the groups we can generate with 999. The value of this number in scientific notation would be (1E3003)-1. The "name" for this number is so long that it would take somewhere between 1 to 2 hours just to say. No one could ever count to such a number as a person would most likely die before even reaching a billion. A trillion is utterly beyond human counting already! and it only gets a thousand times worst with every additional separator ... and there are a thousand separators!! Just for the heck of it, how long would it take some nigh immortal being to count to this number counting at normal human speed? It would take about 1.14*10^2999 years. Even black holes don't take anywhere near this long to completely evaporate. There is no human time frame I can readily compare this to.

    Just understand that already at the end of tier 1 we already have more numbers than we could actually ever use, or have use for. Although numbers of this size and larger are used in the more theoretical areas of physics, by the time we get to numbers of this size exactitude down to the nearest integer is virtually never used. Instead approximate values are used. In this way there are numbers within the first tier range that have never been used and may never be used, even though each one of them individually could be written out in full. Yet we aren't even close to being done with counting in Bowers' Counting System! Let's now continue to Tier 2!

The 2nd Tier Intermediates

    There aren't really many guidelines for how to continue after this. We now enter Bowers system and vastly unexplored territory, so we can't use Conway&Guy as a guide. I contacted Bowers to try to get some feed back. One the reasons he cites for not being interested in the intermediate terms is that they become unwieldingly long. Personally I think that's the most fascinating aspect of them (you'll see what I mean later). In any case he said that it might be worth mentioning some of the shorter ones. He mentions a centiattillion, and a decifemtillion.

    This makes it fairly clear what Bowers probably has in mind, at least for the 2nd tier, where the index of the illion is itself an illion class number.

    Recall earlier that Bowers' defined the thousandth illion as a millillion. He then decided to use the small scale SI prefixes to continue. Namely: micro, nano, pico, femto, atto, zepto, and yocto. Basically what Bowers' comment suggests is that we can use the canonical small scale SI prefixes as Class 2 separators.

    Recall that Class 1 separators were used between "groups" equivalent to Tier 0 constructions. We can call these "Class 0 groups". The Class 0 groups are simply the english number names from 1 to 999. Now the Class 2 separators (small scale SI prefixes) will be used between "modifier groups" which are equivalent to Tier 1 constructions. Tier 1 constructions are the "latin numbers" we used to describe all of the Tier 1 separators. We can call these "Class 1 groups".

    If the pattern is not readily apparent, an example is likely to help the idea along. After a novemnonagintinongentillion would be a millillion. "milli" here is acting just like "thousand" did before. To go to the next illion (the 1001st one), we simply place "one" to the right of milli. How this is done is not exactly spelled out, however I would suggest using milli-untillion. Follow this with milli-duotillion, and this with milli-tretillion. After this, we can simply add "milli" to all of the illions we've already constructed. Next would come milli-quadrillion, milli-quintillion, ... etc. all the way to milli-novemnonagintinongentillion.

    To continue, we now place a Class 1 group to the left of milli. The 2000th illion would be duomillillion. Again we could append a Class 1 group between "milli" and "illion" to represent the "ones group". So we would continue with duomilli-untillion, duomilli-duotillion, duomilli-tretillion, duomilli-quadrillion, etc.

    Beyond all this would be tremillillion, quattuormillillion, quinmillillion, etc. Basically we can describe the first 999,999 illions in the form:

G(1)-milli-G(0)-illion 

where G(1) and G(0) are latin numbers (as described in Tier 1) from 1 to 999.

The value of this expression is then defined as H(G(1)*1000+G(0)) where G(1) and G(0) are interpreted as numeric values

    Using all of the canonical small scale SI prefixes we can form names for the first 999,999,999,999,999,999,999,999,999 illions. They will generally be of the form:

G(8)-yocto-G(7)-zepto-G(6)-atto-G(5)-femto-G(4)-atto-G(3)-nano-G(2)-

micro-G(1)-milli-G(0)-illion

    Just as before we can drop group/separator combos when the group = 0, and G(0) can be dropped when G(0) = 0. When any Class 2 separator is not followed by a group, but by illion, its last vowel can be dropped, as is the case with millillion, micrillion, nanillion, etc.

    It's important to note that any group G(k) where k > 0 can never use the 1st option ones roots. The only time these get used is in the names million, billion, trillion, quadrillion, quintillion, sextillion, septillion, octillion, and nonillion. This applies only to G(0). For any other group, rule 2 must be changed so that the 2nd option ones roots are used, Thus we would have duomillillion, tremillillion, quattuormillillion, quinmillillion, sexmillillion, septenmillion, octomillillion, and novemmillillion. Also note that for any other group other than G(0), when G(k) = 1, a blank is used. For example, the 1,001,000th illion would be micro-millillion. G(0) also acts differently when there are Class 2 separators involved. In this case when G(0) = 1,2,3, we must use "unt", "duot", "tret" respectively instead of "m", "b", and "tr". If G(0) > 3 however, all of the normal rules for Tier 1 apply.

    As far as I can tell the above describes all the rules we will ever need for Class 1 groups from this point onwards. For clarity here is a table with some examples, so you get a better idea of how the above would work:

List of Bowers' Style Low Tier 2 illions

 Bowers' Tier 2 illion
 Scientific Notation
Half-Scale Notation
 millillion 1E3003
H(1000)
milli-untillion
1E3006
H(1001)
 milli-duotillion 1E3009
H(1002)
 milli-tretillion 1E3012
 H(1003)
milli-quadrillion
 1E3015 H(1004)
 milli-quintillion  1E3018  H(1005)
 milli-sextillion  1E3021  H(1006)
 milli-septillion  1E3024  H(1007)
 milli-octillion  1E3027  H(1008)
 milli-nonillion  1E3030  H(1009)
 milli-decillion  1E3033  H(1010)
 milli-undecillion  1E3036  H(1011)
 milli-doedecillion  1E3039  H(1012)
 milli-tredecillion  1E3042  H(1013)
 milli-quattuordecillion  1E3045  H(1014)
 milli-quindecillion  1E3048  H(1015)
 milli-sexdecillion  1E3051  H(1016)
 milli-septendecillion  1E3054  H(1017)
 milli-octodecillion  1E3057  H(1018)
 milli-novemdecillion  1E3060  H(1019)
 milli-vigintillion  1E3063  H(1020)
 milli-unvigintillion  1E3066 H(1021)
 milli-duovigintillion  1E3069  H(1022)
 milli-trevigintillion  1E3072  H(1023)
 milli-quattuorvigintillion  1E3075  H(1024)
 ...  ...  ...
 milli-trigintillion  1E3093  H(1030)
 milli-quadragintillion  1E3123  H(1040)
 milli-quinquagintillion  1E3153  H(1050)
 ...  ...  ...
 milli-centillion  1E3303  H(1100)
 milli-uncentillion  1E3306  H(1101)
 milli-duocentillion  1E3309  H(1102)
 milli-trecentillion  1E3312  H(1103)
 ...  ...  ...
 milli-decicentillion  1E3333  H(1110)
 milli-undecicentillion  1E3336  H(1111)
 milli-doedecicentillion  1E3339  H(1112)
 ...  ...  ...
 milli-viginticentillion  1E3363  H(1120)
 milli-triginticentillion  1E3393  H(1130)
 ...  ...
 ...
 milli-ducentillion  1E3603  H(1200)
 milli-trescentillion  1E3903  H(1300)
 milli-quadringentillion  1E4203  H(1400)
 ...  ...  ...
 milli-novemnonagintinongentillion  1E6000  H(1999)
 duomillillion  1E6003  H(2000)
 duomilli-untillion  1E6006  H(2001)
 duomilli-duotillion  1E6009  H(2002)
 duomilli-tretillion  1E6012  H(2003)
 duomilli-quadrillion  1E6015  H(2004)
 ...  ...  ...
 tremillillion  1E9003  H(3000)
 quattuormillillion  1E12,003  H(4000)
 quinmillillion  1E15,003  H(5000)
 sexmillillion  1E18,003  H(6000)
 septenmillillion  1E21,003  H(7000)
 octomillillion  1E24,003  H(8000)
 novemmillillion  1E27,003  H(9000)
 decimillillion
 1E30,003  H(10,000)
 undecimillillion 1E33,003
 H(11,000)
 duodecimillillion  1E36,003  H(12,000)
 tredecimillillion  1E39,003  H(13,000)
 quattuordecimillillion  1E42,003  H(14,000)
...
 ... ...
vigintimillillion
 1E60,003 H(20,000)
 trigintimillillion  1E90,003  H(30,000)
 ...  ...  ...
 centimillillion  1E300,003  H(100,000)
 ducentimillillion  1E600,003  H(200,000)
 trescentimillillion  1E900,003  H(300,000)
 ...  ...  ...
 novemnonagintinongentimilli-novemnonagintinongentillion  1E3,000,000  H(999,999)
 micrillion  1E3,000,003  H(1,000,000)
 micro-untillion  1E3,000,006  H(1,000,001)
 micro-duotillion  1E3,000,009  H(1,000,002)
 micro-tretillion  1E3,000,012  H(1,000,003)
 ...  ...  ...
 micro-millillion  1E3,003,003  H(1,001,000)
 micro-milli-untillion  1E3,003,006  H(1,001,001)
 micro-milli-duotillion  1E3,003,009  H(1,001,002)
 micro-milli-tretillion  1E3,003,012  H(1,001,003)
 ...  ...  ...
 micro-duomillillion  1E3,006,003  H(1,002,000)
 micro-tremillillion  1E3,009,003  H(1,003,000)
 ...  ...  ...
 micro-decimillillion  1E3,030,003  H(1,010,000)
 micro-undecimillillion  1E3,033,003  H(1,011,000)
 micro-doedecimillillion  1E3,036,003  H(1,012,000)
 ...  ...  ...
 micro-vigintimillillion  1E3,060,003
 H(1,020,000)
 micro-trigintimillillion  1E3,090,003  H(1,030,000)
 ...  ...  ...
 micro-centimillillion  1E3,300,003  H(1,100,000)
 micro-ducentimillillion  1E3,600,003  H(1,200,000)
 ...  ...  ...
 micro-novemnonagintinongentimilli-novemnonagintinongentillion  1E6,000,000  H(1,999,999)
 duomicrillion  1E6,000,003  H(2,000,000)
 duomicro-untillion 1E6,000,006
 H(2,000,001)
 ...  ...  ...
 tremicrillion  1E9,000,003  H(3,000,000)
 quattuormicrillion  1E12,000,003  H(4,000,000)
 quinmicrillion  1E15,000,003  H(5,000,000)
 ...  ...  ...
 decimicrillion  1E30,000,003  H(10,000,000)
 undecimicrillion  1E33,000,003  H(11,000,000)
 doedecimicrillion  1E36,000,003  H(12,000,000)
 ...  ...  ...
 vigintimicrillillion  1E60,000,003  H(20,000,000)
 trigintimicrillion  1E90,000,003  H(30,000,000)
 quadragintimicrillion  1E120,000,003  H(40,000,000)
 ...  ...  ...
 centimicrillion  1E300,000,003  H(100,000,000)
 ducentimicrillion  1E600,000,003  H(200,000,000)
 trescentimicrillion  1E900,000,003  H(300,000,000)
 ...  ...  ...
 novemnonagintinongentimicro-novemnonagintinongentimilli-novemnonagintinongentillion 1E3,000,000,000
 H(999,999,999)
 nanillion  1E3,000,000,003  H(1,000,000,000)
 nano-untillion  1E3,000,000,006  H(1,000,000,001)
 nano-duotillion  1E3,000,000,009  H(1,000,000,002)
 nano-tretillion  1E3,000,000,012  H(1,000,000,003)
 nano-quadrillion  1E3,000,000,015  H(1,000,000,004)
 ...  ...  ...
 nano-millillion  1E3,000,003,003  H(1,000,001,000)
 ...  ... ...
 nano-micrillion  1E3,003,000,003  H(1,001,000,000)
 ...  ...  ...
 nano-micro-millillion  1E3,003,003,003  H(1,001,001,000)
 ...  ...  ...
 duonanillion  1E6,000,000,003  H(2,000,000,000)
 trenanillion  1E9,000,000,003  H(3,000,000,000)
 ...  ...  ...
 decinanillion  1E30,000,000,003  H(10,000,000,000)
 vigintinanillion 1E60,000,000,003
H(20,000,000,000)
 ...  ...  ...
 centinanillion  1E300,000,000,003  H(100,000,000,000)
 ...  ...  ...
 novemnonagintinongentinano-novemnonagintinongentimicro-novemnonagintinongentimilli-novemnonagintinongentillion  1E3,000,000,000,000  H(999,999,999,999)
 picillion  1E3,000,000,000,003 H(1,000,000,000,000)
 pico-untillion  1E3,000,000,000,006  H(1,000,000,000,001)
 ...  ...  ...
 pico-millillion  1E3,000,000,003,003  H(1,000,000,001,000)
 ...  ...  ...
 pico-micrillion  1E3,000,003,000,003  H(1,000,001,000,000)
 ...  ...  ...
 pico-micro-millillion  1E3,000,003,003,003  H(1,000,001,001,000)
 ...  ...  ...
 pico-nanillion  1E3,003,000,000,003  H(1,001,000,000,000)
 ...  ...  ...
 pico-nano-millillion  1E3,003,000,003,003  H(1,001,000,001,000)
 ...  ...  ...
 pico-nano-micrillion  1E3,003,003,000,003  H(1,001,001,000,000)
 ...  ...  ...
 pico-nano-micro-millillion  1E3,003,003,003,003  H(1,001,001,001,000)
 ...  ...  ...
 duopicillion  1E6,000,000,000,003  H(2,000,000,000,000)
 trepicillion  1E9,000,000,000,003  H(3,000,000,000,000)
 ...  ...  ...
 decipicillion  1E30,000,000,000,003  H(10,000,000,000,000)
 vigintipicillion  1E60,000,000,000,003  H(20,000,000,000,000)
 ...  ...  ...
 centipicillion  1E300,000,000,000,003  H(100,000,000,000,000)
 ...  ...  ...
 novemnonagintinongentipico-novemnonagintinongentinano-novemnonagintinongentimicro-novemnonagintinongentimilli-novemnonagintinongentillion  1E3,000,000,000,000,000  H(999,999,999,999,999)
 femtillion 1E3,000,000,000,000,003
 H(1,000,000,000,000,000)
 femto-untillion  1E3,000,000,000,000,006  H(1,000,000,000,000,001)
...
 ...  ...
 femto-millillion  1E3,000,000,000,003,003  H(1,000,000,000,001,000)
 femto-milli-untillion  1E3,000,000,000,003,006  H(1,000,000,000,001,001)
 ...  ...  ...
 femto-micrillion  1E3,000,000,003,000,003  H(1,000,000,001,000,000)
 femto-micri-millillion  1E3,000,000,003,003,003  H(1,000,000,001,001,000)
 femto-nanillion  1E3,000,003,000,000,003  H(1,000,001,000,000,000)
 femto-nano-micrillion  1E3,000,003,003,000,003
 H(1,000,001,001,000,000)
femto-nano-micro-millillion
1E3,000,003,003,003,003
 H(1,000,001,001,001,000)
 femto-nano-micro-milli-untillion 1E3,000,003,003,003,006
 H(1,000,001,001,001,001)
 femto-picillion 1E3,003,000,000,000,003
 H(1,001,000,000,000,000)
 femto-pico-nanillion 1E3,003,003,000,000,003
 H(1,001,001,000,000,000)
 femto-pico-nano-micrillion  1E3,003,003,003,000,003  H(1,001,001,001,000,000)
 femto-pico-nano-micro-millillion  1E3,003,003,003,003,003  H(1,001,001,001,001,000)
 femto-pico-nano-micro-milli-untillion  1E3,003,003,003,003,006  H(1,001,001,001,001,001)
 ...  ...  ...
 novemnonagintinongentifemto-novemnonagintinongentinano-novemnonagintinongentimicro-novemnonagintinongentimilli-novemnonagintinongentillion  1E3,000,000,000,000,000,000  H(999,999,999,999,999,999)
 attillion 1E3,000,000,000,000,000,003
H(1,000,000,000,000,000,000)
 atto-untillion  1E3,000,000,000,000,000,006  H(1,000,000,000,000,000,001)
 ... ...
...
 atto-femtillion  1E3,003,000,000,000,000,003  H(1,001,000,000,000,000,000)
 atto-femto-picillion  1E3,003,003,000,000,000,003  H(1,001,001,000,000,000,000)
 atto-femto-pico-nanillion  1E3,003,003,003,000,000,003  H(1,001,001,001,000,000,000)
 atto-femto-pico-nano-micrillion  1E3,003,003,003,003,000,003  H(1,001,001,001,001,000,000)
 atto-femto-pico-nano-micro-millillion  1E3,003,003,003,003,003,003  H(1,001,001,001,001,001,000)
atto-femto-pico-nano-micro-milli-untillion 1E3,003,003,003,003,003,006
 H(1,001,001,001,001,001,001)
 novemnonagintinongentiatto-novemnonagintinongentifemto-novemnonagintinongentipico-novemnonagintinongentinano-novemnonagintinongentimicro-novemnonagintinongentimilli-novemnonagintinongentillion  1E3,000,000,000,000,000,000,000  H(999,999,999,999,999,999,999)
 zeptillion 1E3,000,000,000,000,000,000,003
H(H(6))
 zepto-untillion  1E3,000,000,000,000,000,000,006  H(H(6)+1)
 ...  ...  ...
 zepto-attillion  1E3,003,000,000,000,000,000,003  H(H(6)+H(5))
 zepto-atto-femtillion  1E3,003,003,000,000,000,000,003  H(H(6)+H(5)+H(4))
 zepto-atto-femto-picillion  1E3,003,003,003,000,000,000,003  H(H(6)+H(5)+H(4)+H(3))
 zepto-atto-femto-pico-nanillion  1E3,003,003,003,003,000,000,003  H(H(6)+H(5)+H(4)+H(3)+...
...H(2))
 zepto-atto-femto-pico-nano-micrillion  1E3,003,003,003,003,003,000,003  H(H(6)+H(5)+H(4)+H(3)+...
...H(2)+H(1))
 zepto-atto-femto-pico-nano-micro-millillion  1E3,003,003,003,003,003,003,003  H(H(6)+H(5)+H(4)+H(3)+...
...H(2)+H(1)+1000)
 zepto-atto-femto-pico-nano-micro-milli-untillion  1E3,003,003,003,003,003,003,006  H(H(6)+H(5)+H(4)+H(3)+...
...H(2)+H(1)+1001)
 ... ...
...
 novemnonagintinongentizepto-novemnonagintinongentiatto-novemnonagintinongentifemto-novemnonagintinongentipico-novemnonagintinongentinano-novemnonagintinongentimicro-novemnonagintinongentimilli-novemnonagintinongentillion  1E(3E24) H(H(7)-1)
yoctillion
 1E(3E24+3)  H(H(7))
 yocto-untillion  1E(3E24+6)  H(H(7)+1)
 ...  ...  ...
 yocto-zeptillion  1E(3E24+3E21+3)  H(H(7)+H(6))
 yocto-zepto-attillion  1E(3E24+3E21+3E18+3)  H(H(7)+H(6)+H(5))
 yocto-zepto-atto-femtillion  1E(3E24+3E21+3E18+3E15+3)  H(H(7)+H(6)+H(5)+H(4))
 yocto-zepto-atto-femto-picillion  1E(3E24+3E21+3E18+3E15+ ...
... 3E12+3)
 H(H(7)+H(6)+H(5)+H(4)+ ...
... H(3))
 yocto-zepto-atto-femto-pico-nanillion 1E(3E24+3E21+3E18+3E15+ ...
... 3E12+3E9+3)
 H(H(7)+H(6)+H(5)+H(4)+ ...
... H(3)+H(2))
yocto-zepto-atto-femto-pico-nano-micrillion
1E(3E24+3E21+3E18+3E15+ ...
... 3E12+3E9+3E6+3)
 H(H(7)+H(6)+H(5)+H(4)+ ...
... H(3)+H(2)+H(1))
 yocto-zepto-atto-femto-pico-nano-micro-millillion  1E(3E24+3E21+3E18+3E15+ ...
... 3E12+3E9+3E6+3E3+3)
 H(H(7)+H(6)+H(5)+H(4)+ ...
... H(3)+H(2)+H(1)+1000)
 yocto-zepto-atto-femto-pico-nano-micro-milli-untillion  1E(3E24+3E21+3E18+3E15+ ...
... 3E12+3E9+3E6+3E3+6)
 H(H(7)+H(6)+H(5)+H(4)+ ...
... H(3)+H(2)+H(1)+1001)
novemnonagintinongentiyocto-novemnonagintinongentizepto-novemnonagintinongentiatto-novemnonagintinongentifemto-novemnonagintinongentipico-novemnonagintinongentinano-novemnonagintinongentimicro-novemnonagintinongentimilli-novemnonagintinongentillion 1E(3E27)
H(H(8)-1)

    The last entry is the largest illion we can name using only the canonical SI prefixes. The largest number that we can name by using only the canonical SI prefixes would be :

" 999 novemnonagintinongentiyocto-novemnonagintinongentizepto-novemnonagintinongentiatto-novemnonagintinongentifemto-novemnonagintinongentipico-novemnonagintinongentinano-novemnonagintinongentimicro-novemnonagintinongentimilli-novemnonagintinongentillion 999 novemnonagintinongentiyocto-novemnonagintinongentizepto-novemnonagintinongentiatto-novemnonagintinongentifemto-novemnonagintinongentipico-novemnonagintinongentinano-novemnonagintinongentimicro-novemnonagintinongentimilli-octononagintinongentillion 999 novemnonagintinongentiyocto-novemnonagintinongentizepto-novemnonagintinongentiatto-novemnonagintinongentifemto-novemnonagintinongentipico-novemnonagintinongentinano-novemnonagintinongentimicro-novemnonagintinongentimilli-septennonagintinongentillion 999 novemnonagintinongentiyocto-novemnonagintinongentizepto-novemnonagintinongentiatto-novemnonagintinongentifemto-novemnonagintinongentipico-novemnonagintinongentinano-novemnonagintinongentimicro-novemnonagintinongentimilli-sexnonagintinongentillion 999 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 999 quadrillion 999 trillion 999 billion 999 million 999 thousand 999 "

    This number would be 1E(3E27+3)-1. The "name" for this number is so long that it would take something like seventy billion times the current age of the universe just to say! In decimal it has 3 octillion and 3 digits, all 9s. And this is not even the longest number name that can be constructed using Bowers nomenclature!

    After this point however we do run into the problem of what to do next. It is clear that if we can create a series of Class 2 separators we can express any illion number in the form:

G(n)-H(n-1)-G(n-1)-H(n-2)- ... ... -G(2)-H(1)-G(1)-H(0)-G(0)-illion

and this will correspond to the number:

 H(G(n)*H(n-1) + G(n-1)*H(n) + ... G(2)*H(1) + G(1)*H(0) + G(0))

    The problem is we have already exhausted the canonical SI prefixes. To continue we can follow Bowers system and create new prefixes. For example, his next milestone illion after a yoctillion is a xonillion. By dropping the illion and adding "o" we can create a bunch of additional prefixes. Namely, we can continue after yocto with:

xono, veco, meco, dueco, treco, tetreco, penteco, hexeco, hepteco, octeco, enneco, icoso, ...

    After this however, Bowers starts to skip prefixes, and jump by 10s. This leaves us with the problem of figuring out how to construct the prefixes between the 20th and 30th prefix.

    Although there is no clear cut way to do this based on Bowers milestones, I'm going to go out on a limb and guess that the following sequence is a pretty close fit:

meicoso, dueicoso, trioicoso, tetreicoso, penteicoso, hexeicoso, hepteicoso, octeicoso, enneicoso,...

   
Essentially I can use me, due, trio, tetre, pente, hexe, hepte, octe, and enne, as the ones root for the 2nd Tier. This follows pretty closely the examples Bowers' does provide for the 11th through 19th prefix with one notable exception. Instead of using "tre" I have used "trio". If "tre" is used this is identical to the root for "3" used at Tier 1. This would make an expression such as treicosillion ambiguous. Does this mean the 3E60 illion, or the 1E69 illion? By labeling the 1E69 illion as trioicosillion we avoid this snag. The tens roots can be obtained from Bowers milestone illions. After icoso would come:

triaconto, tetraconto, pentaconto, hexaconto, heptaconto, octaconto, ennaconto, ...

    Finally we need the hundreds roots to complete the 2nd Tier. Unfortunately Bowers only provides the 100th prefix of hecto, and not the 200th, 300th, 400th, etc. prefix. We can guess however that these can again be constructed using the greek prefixes. Namely we would have:

hecto, dohecto, triahecto, tetrahecto, pentahecto, hexahecto, heptahecto, octahecto, ennahecto,...

    These terms are very similar to what we would obtain with the 102nd, 103rd, 104th, etc. prefix. To distinguish them I end the greek prefixes with an "a" instead of "e" as with the ones roots. This avoids the potential ambiguity. We thus have a complete set of roots for the 2nd Tier. For convenience we can gather these into a single table for easy reference:

Bowers' Tier 2 Roots

 Value 2nd Ones Root
2nd Tens Root
2nd Hundreds Root
 1  mill(i)/me vec(o,e)/c(o,e)
hect(o)
 2  micr(o)/due  icos(o,e)  dohect(o)
 3  nan(o)/tre/trio  triacont(o,e)  triahect(o)
 4  pic(o)/tetre  tetracont(o,e)  tetrahect(o)
 5  femt(o)/pente  pentacont(o,e)  pentahect(o)
 6  att(o)/hexe  hexacont(o,e)  hexahect(o)
 7  zept(o)/hepte  heptacont(o,e)  heptahect(o)
 8  yoct(o)/octe  octacont(o,e)  octahect(o)
 9  xon(o)/enne  ennacont(o,e)  ennahect(o)

    The 2nd Tier roots are not quite as simple as the 1st Tier roots. Note that the SI prefixes are only used for the first 9 prefixes. After this, the system looks very similar to a greek based system. This is why some of Bowers names are identical to numbers named in Russ Rowletts system. However Bowers versions are vastly larger!

    The following rules can be used to generate the nth Class 2 Separator:

1. If hundreds and tens = 0, then use 1st option ones root. (include vowel if followed by a group, and drop vowel if followed by illion)

2. If hundreds = 0 and tens = 1, use veco if ones = 0, and use 2nd option ones root followed by "co" otherwise.

3. If hundreds = 0 and tens > 1, use 3rd option ones followed by tens root ending in "o"

4. If hundreds > 0 and tens = 0, then use 3rd option ones followed by hundreds ending in "o"

5. If hundreds > 0 and tens = 1, if ones = 0 use vece followed by hundreds ending in "o", otherwise use 2nd option ones root followed by "ce" followed by hundreds ending in "o"

6. If hundreds > 0 and tens > 1, use 3rd option ones root followed by tens root ending in "e" followed by hundreds root ending in "o".


    To the best of my knowledge the above rules allow the naming of every number up to the limit of Tier 2 without ambiguity. In order for a illion system to be non-ambiguous, every power of a thousand must have a unique name, and every legal name must name a unique number. Essentially there must be a one-to-one correspondence between the numbers and their names.

    Although it starts to get a bit confusing we can consider some examples within the 2nd Tier range to show how this would work in practice. In the following table we will finish up the 2nd Tier illions. This will provide evidence that the system is in fact free of ambiguities up to this point:

Bowers' Style 2nd Tier illions

 Bowers'
2nd Tier illions
 Scientific Notation
Half-Scale Notation
 xonillion 1E(3E27+3)
H(H(8))
 xono-yocto-zepto-atto-femto-pico-nano-micro-millillion 1E(3E27+3E24+3E21+3E18+3E15+3E12 ...
+3E9+3E6+3E3+3)
H(H(8)+H(7)+H(6)+H(5)+H(4)+H(3)+
...
H(2)+H(1)+1000)
 vecillion 1E(3E30+3)
H(H(9))
 veco-xono-yocto-zepto-atto-femto-pico-nano-micro-millillion 1E(3E30+3E27+3E24+3E21+3E18+3E15 ...
+3E12+3E9+3E6+3E3+3)
H(H(9)+H(8)+H(7)+H(6)+H(5)+H(4)+
...
H(3)+H(2)+H(1)+1000) 
mecillion
1E(3E33+3)
 H(H(10))
 meco-veco-xono-yocto-zepto-atto-femto-pico-nano-micro-millillion 1E(3E33+3E30+3E27+3E24+3E21+3E18
...
+3E15+3E12+3E9+3E6+3E3+3) 
 H(H(10)+H(9)+H(8)+H(7)+H(6)+H(5)+
...
H(4)+H(3)+H(2)+H(1)+1000) 
 duecillion  1E(3E36+3)  H(H(11))
 dueco-meco-veco-xono-yocto-zepto-atto-femto-pico-nano-micro-millillion  1E(3E36+3E33+3E30+3E27+3E24+3E21
...
+3E18+3E15+3E12+3E9+3E6+3E3+3)
 H(H(11)+H(10)+H(9)+H(8)+H(7)+H(6)
...
+H(5)+H(4)+H(3)+H(2)+H(1)+1000)
 trecillion  1E(3E39+3)  H(H(12))
 treco-dueco-meco-veco-xono-yocto-zepto-atto-femto-pico-nano-micro-millillion  1E(3E39+3E36+3E33+3E30+3E27+3E24
...
+3E21+3E18+3E15+3E12+3E9+3E6+
...
3E3+3)
H(H(12)+H(11)+H(10)+H(9)+H(8)+
...
H(7)+H(6)+H(5)+H(4)+H(3)+H(2)+
...
H(1)+1000)
 tetrecillion  1E(3E42+3)  H(H(13))
 tetreco-treco-dueco-meco-veco-xono-yocto-zepto-atto-femto-pico-nano-micro-millillion  1E(3E42+3E39+3E36+3E33+3E30+3E27
...
+3E24+3E21+3E18+3E15+3E12+3E9+
...
3E6+3E3+3)
H(H(13)+H(12)+H(11)+H(10)+H(9)+
...
H(8)+H(7)+H(6)+H(5)+H(4)+H(3)+
...
H(2)+H(1)+1000) 
 ... ...
...
 icosillion  1E(3E60+3)  H(H(19))
 icoso-enneco-octeco-hepteco-hexeco-penteco-tetreco-treco-dueco-meco-veco-xono-yocto-zepto-atto-femto-pico-nano-micro-millillion  1E(3E60+3E57+3E54+3E51+3E48+3E45
...
+3E42+3E39+3E36+3E33+3E30+3E27+
...
3E24+3E21+3E18+3E15+3E12+3E9+
...
3E6+3E3+3)
H(H(19)+H(18)+H(17)+H(16)+H(15)
...
+H(14)+H(13)+H(12)+H(11)+H(10)+
...
H(9)+H(8)+H(7)+H(6)+H(5)+H(4)+
...
H(3)+H(2)+H(1)+1000)
 ...  ... ...
treicosillion
1E(9E60+3)
 H(3*H(19))
 ...  ... ...
 trioicosillion  1E(3E69+3)  H(H(22))
...
 ...  ...
 triacontillion  1E(3E90+3)  H(H(29))
 triaconto-enneicoso-octeicoso-hepteicoso-hexeicoso-penteicoso-tetreicoso-trioicoso-dueicoso-meicoso-icoso-enneco-octeco-hepteco-hexeco-penteco-tetreco-treco-dueco-meco-veco-xono-yocto-zepto-atto-femto-pico-nano-micro-millillion 1E(3E90+3E87+3E84+3E81+3E78+3E75
...
+3E72+3E69+3E66+3E63+3E60+3E57+
...
3E54+3E51+3E48+3E45+
...
3E42+3E39+3E36+3E33+3E30+3E27+
...
3E24+3E21+3E18+3E15+3E12+3E9+
...
3E6+3E3+3)
H(H(29)+H(28)+H(27)+H(26)+H(25)
...
+H(24)+H(23)+H(22)+H(21)+H(20)+
...
 H(19)+H(18)+H(17)+H(16)+H(15)+
...
H(14)+H(13)+H(12)+H(11)+H(10)+
...
H(9)+H(8)+H(7)+H(6)+H(5)+H(4)+
...
H(3)+H(2)+H(1)+1000)
 ...  ... ...
 tetracontillion  1E(3E120+3)  H(H(39))
 ...  ...  ...
 pentacontillion  1E(3E150+3)  H(H(49))
 ...  ...  ...
 hexacontillion  1E(3E180+3) H(H(59))
 ...  ...  ...
 heptacontillion 1E(3E210+3)
 H(H(69))
 ...  ...  ...
 octacontillion  1E(3E240+3)  H(H(79))
 ...  ...  ...
 ennacontillion  1E(3E270+3)  H(H(89))
 ...  ...  ...
 hectillion  1E(3E300+3)  H(H(99))
hecto-millillion
1E(3E300+3003)
H(H(99)+1000)
hecto-enneennaconto-octeennaconto-hepteennaconto-hexeennaconto-penteennaconto-tetreennaconto-trioennaconto-dueennaconto-meennaconto-ennaconto-enneoctaconto-octeoctaconto-hepteoctaconto-
...
octaconto-
enneheptaconto-octeheptaconto-
...
heptaconto-
ennehexaconto-
...
hexaconto-
ennepentaconto-
...
pentaconto-
...
tetraconto-
...
triaconto-
...
icoso-
enneicoso-
...
veco-xono-yocto-zepto-atto-femto-pico-nano-micro-millillion
1E(3E300+3E297+3E294+3E291+3E288
...
+3E285+3E282+3E279+3E276+3E273+
...
3E270+3E267+3E264+3E261+
...
3E240+3E237+3E234+
...
3E210+3E207+
...
3E180+3E177+
...
3E150+
...
3E120+
...
3E90+
...
3E60+3E57
...
3E30+3E27+3E24+3E21+3E18+
...
3E15+3E12+3E9+3E6+3E3+3)

 
H(H(99)+H(98)+H(97)+H(96)+H(95)+
...
H(94)+H(93)+H(92)+H(91)+H(90)+
...
H(89)+H(88)+H(87)+H(86)+
...
H(79)+H(78)+H(77)+
...
H(69)+H(68)+
...
H(59)+H(58)+
...
H(49)+
...
H(39)+
...
H(29)+
...
H(19)+H(18)+
...
H(9)+H(8)+H(7)+H(6)+H(5)+
...
H(4)+H(3)+H(2)+H(1)+1000)
 mehectillion 1E(3E303+3)
H(H(100))
 mehecto-millillion  1E(3E303+3003)  H(H(100)+1000)
 duehectillion  1E(3E306+3)  H(H(101))
 duehecto-millillion  1E(3E306+3003)  H(H(101)+1000)
 triohectillion  1E(3E309+3)  H(H(102))
 triohecto
-millillion
 1E(3E309+3003)
 H(H(102)+1000)
 tetrehectillion  1E(3E312+3)  H(H(103))
 tetrehecto-millillion  1E(3E312+3003)  H(H(103)+1000)
 pentehectillion  1E(3E315+3)  H(H(104))
 pentehecto-millillion  1E(3E315+3003)  H(H(104)+1000)
 hexehectillion  1E(3E318+3)  H(H(105))
 hexehecto-millillion  1E(3E318+3003)  H(H(105)+1000)
 heptehectillion  1E(3E321+3)  H(H(106))
 heptehecto-millillion  1E(3E321+3003)  H(H(106)+1000)
 octehectillion  1E(3E324+3)  H(H(107))
 octehecto-millillion  1E(3E324+3003)  H(H(107)+1000)
 ennehectillion  1E(3E327+3)  H(H(108))
 ennehecto-millillion  1E(3E327+3003)  H(H(108)+1000)
 vecehectillion  1E(3E330+3)  H(H(109))
 vecehecto-millillion  1E(3E330+3003)  H(H(109)+1000)
 mecehectillion  1E(3E333+3)  H(H(110))
 duecehectillion  1E(3E336+3)  H(H(111))
 trecehectillion  1E(3E339+3)  H(H(112))
 tetrecehectillion  1E(3E342+3)  H(H(113))
 pentecehectillion  1E(3E345+3)  H(H(114))
 hexecehectillion  1E(3E348+3)  H(H(115))
 heptecehectillion  1E(3E351+3)  H(H(116))
 octecehectillion  1E(3E354+3)  H(H(117))
 ennecehectillion  1E(3E357+3)  H(H(118))
icosehectillion
 1E(3E360+3)  H(H(119))
 meicosehectillion  1E(3E363+3)  H(H(120))
 dueicosehectillion  1E(3E366+3)  H(H(121))
 trioicosehectillion  1E(3E369+3)  H(H(122))
 ...  ...  ...
 triacontehectillion  1E(3E390+3)  H(H(129))
 ...  ...  ...
 tetracontehectillion  1E(3E420+3)  H(H(139))
 ...  ...  ...
 pentacontehectillion  1E(3E450+3)  H(H(149))
 ...  ...  ...
 hexacontehectillion  1E(3E480+3)  H(H(159))
 ...  ...  ...
 heptacontehectillion  1E(3E510+3)  H(H(169))
 ...  ...  ...
 octacontehectillion  1E(3E540+3)  H(H(179))
 ...  ...  ...
 ennacontehectillion  1E(3E570+3)  H(H(189))
 ...  ...  ...
 dohectillion  1E(3E600+3)  H(H(199))
 medohectillion  1E(3E603+3)  H(H(200))
 duedohectillion  1E(3E606+3)  H(H(201))
 triodohectillion
 1E(3E609+3)  H(H(202))
 tetredohectillion  1E(3E612+3)  H(H(203))
 ...  ...  ...
 vecedohectillion  1E(3E630+3)  H(H(209))
 mecedohectillion  1E(3E633+3)  H(H(210))
 duecedohectillion  1E(3E636+3)  H(H(211))
 trecedohectillion  1E(3E639+3)  H(H(212))
 ...  ...  ...
 icosedohectillion  1E(3E660+3)  H(H(219))
triacontedohectillion
 1E(3E690+3)  H(H(229))
 tetraconte-dohectillion  1E(3E720+3)  H(H(239))
pentaconte-dohectillion
 1E(3E750+3)  H(H(249))
 ...  ...  ...
 triahectillion  1E(3E900+3)  H(H(299))
 metriahectillion  1E(3E903+3)  H(H(300))
 ...  ...  ...
 tetrahectillion  1E(3E1200+3)  H(H(399))
 tetretetrahectillion  1E(3E1212+3)  H(H(403))
 ...  ...  ...
 pentahectillion  1E(3E1500+3)  H(H(499))
pentepentahectillion
 1E(3E1515+3)  H(H(504))
 ...  ...  ...
 hexahectillion  1E(3E1800+3)  H(H(599))
 hexehexahectillion  1E(3E1818+3)  H(H(605))
 ...  ...  ...
 heptahectillion  1E(3E2100+3)  H(H(699))
 hepteheptahectillion  1E(3E2121+3)  H(H(706))
 ...  ...  ...
 octahectillion  1E(3E2400+3)  H(H(799))
 octeoctahectillion  1E(3E2424+3)  H(H(807))
 ...  ...  ...
 ennahectillion  1E(3E2700+3)  H(H(899))
 enneennahectillion  1E(3E2727+3)  H(H(908))
 ...  ...  ...
 enneennaconteenna-hectillion  1E(3E2997+3)  H(H(998))
enneennaconte-
ennahecto-
octeennaconte-
ennahecto-
hepteennaconte-
ennahecto-
hexeennaconte-
ennahecto-

...

ennahecto-

...

octahecto-

...

heptahecto-

...

hexahecto-

...

pentahecto-

...

tetrahecto-

...

triahecto-

...

dohecto-

...

hecto-
enneennaconto-
octeennaconto-
hepteennaconto-
hexeennaconto-
...
ennaconto-
...
octaconto-
...
heptaconto-
...
hexaconto-
...
pentaconto-
...
tetraconto-
...
triaconto-
...
icoso-
enneco-
octeco-
hepteco-
hexeco-
penteco-
tetreco-
treco-
dueco-
meco-
veco-xono-yocto-zepto-atto-femto-pico-nano-micro-milli-untillion
 1E(3E2997+3E2994+3E2991+3E2988+

...

3E2700+

...

3E2400+

...

3E2100+

...

3E1800+

...

3E1500+

...

3E1200+

...

3E900+

...

3E600+

...

3E300+3E297+3E294+3E291+3E288+
...
3E270+
...
3E240+
...
3E210+
...
3E180+
...
3E150+
...
3E120+
...
3E90+
...
3E60+3E57+3E54+3E51+3E48+3E45+
3E42+3E39+3E36+3E33+3E30+3E27+
3E24+3E21+3E18+3E15+3E12+3E9+
3E6+3E3+6)


H(H(998)+H(997)+H(996)+H(995)+

...

H(899)+

...

H(799)+

...

H(699)+

...

H(599)+

...

H(499)+

...

H(399)+

...

H(299)+

...

H(199)+

...

H(99)+H(98)+H(97)+H(96)+H(95)+
...
H(89)+
...
H(79)+
...
H(69)+
...
H(59)+
...
H(49)+
...
H(39)+
...
H(29)+
...
H(19)+H(18)+H(17)+H(16)+H(15)+
H(14)+H(13)+H(12)+H(11)+H(10)+
H(9)+H(8)+H(7)+H(6)+H(5)+H(4)+
H(3)+H(2)+H(1)+1001)
 novemnonaginti-nongenti-
enneennaconte-
ennahecto-

novemnonaginti-nongenti-
octeennaconte-
ennahecto-

novemnonaginti-nongenti-
hepteennaconte-
ennahecto-

novemnonaginti-
nongenti-
hexeennaconte-
ennahecto-

novemnonaginti-
nongenti-
penteennaconte-
ennahecto-


...

novemnonaginti-
nongenti-
ennahecto-
novemnonaginti-
nongenti-
enneennaconte-
octahecto-


...

novemnonaginti-
nongenti-
octahecto-
novemnonaginti-
nongenti-
enneennaconte-
heptahecto-


...

novemnonaginti-
nongenti-
heptahecto-

...

novemnonaginti-
nongenti-
hexahecto-

...

novemnonaginti-
nongenti-
pentahecto-

...

novemnonaginti
nongenti-
tetrahecto-

...

novemnonaginti-
nongenti-
triahecto-

...

novemnonaginti-
nongenti-
dohecto-

...

novemnonaginti-
nongenti-
hecto-
novemnonaginti-
nongenti-
enneennaconto-
novemnonaginti-
nongenti-
octeennaconto-

...

novemnonaginti-
nongenti-
icoso-
novemnonaginti-
nongenti-
enneco-
novemnonaginti-nongenti-
octeco-
novemnonaginti-
nongenti-
hepteco-
novemnonaginti-
nongenti-
hexeco-
novemnonaginti-
nongenti-
penteco-
novemnonaginti-
nongenti-
tetreco-
novemnonaginti-
nongenti-
treco-
novemnonaginti-
nongenti-
dueco-
novemnonaginti-
nongenti-
meco-
novemnonaginti
nongenti-
veco-
novemnonaginti-
nongenti-
xono-
novemnonaginti-
nongenti-
yocto-
novemnonaginti-
nongenti-
zepto-
novemnonaginti-
nongenti-
atto-
novemnonaginti-
nongenti-
femto-
novemnonaginti-
nongenti-
pico-
novemnonaginti-
nongenti-
nano-
novemnonaginti-
nongenti-
micro-
novemnonaginti-
nongenti-
milli-
novemnonaginti-
nongentillion
1E(3E3000)
H(H(999)-1)

 The last entry is the largest illion that can be named in Bowers system within the 2nd Tier. The name is very long, containing 40,684 letters! It would probably take about one and a half hours just to say! The largest number that we can name within the 2nd Tier would be:

999 novemnonagintinongentienneenneconteennahecto- ... ... ... milli-novemnonagintinongentillion 999 novemnonagintinongentienneenneconteennahecto- ... ... ... milli-octononagintinongentillion 999 novemnonagintinongentienneenneconteennahecto- ... ... ... milli-septenmnonagintinongentillion

... ... ... ... ... ...

... ... ... ... ... ...

... ... ... ... ... ...

999 quadrillion 999 trillion 999 billion 999 million 999 thousand 999

    In otherwords, filling every group with 999 for every illion name we can so far construct. So far we can construct 1E3000-1 such names! This means the largest number we can name so far is a number so long that it would take roughly 1E3000 hours to say. That's the same as 1.141E2996 years. That's also 8.323E2985 times the current age of our universe. Basically its a length of time so long that nothing in our familiar reality can compare or properly hint at the time frame involved, ... and this is just to say the name! Recall that the largest Tier 1 number takes about this long to count to. These numbers are now so large that just saying the name of the last 2nd Tier number takes as long as it takes to count to a millillion! Now try to imagine how long it would take to count to this number!!

    The vast majority of numbers within this range will be whoppers like the above. In fact we can make some estimate on how many of the numbers from 1 to the largest Tier 2 number will have the majority of its digits non-zero. Numbers containing less than half the number of non-zero digits as the largest Tier 2 number account for a mere 1E(-5.97E3001) % of all the numbers from 1 to the largest Tier 2 number. You may want to let that last sentence sink in. It means that a vanishingly small fraction of the numbers you would have to count would be short enough to actually say in a time less than the life expectancy of the entire universe, even under generous theoretical models!!

    We can therefore estimate the amount of time it would take to count up to this number by assuming they all take roughly 1E3000 hours to say. Interestingly however, it turns out that there are so many numbers that it barely matters how long it takes to say each individually! Whether it takes a nanosecond for each or 1E2996 years makes no significant difference. We will still get a time frame very close to 10^(10^3000) years! A number of years that does not, in fact, differ in a discernible way from the number we are counting to, even if it takes much less or much more than a year, on average, to say any particular number. How can a time frame like this be comprehended?! It can't. However this analogy might help you get a better idea how long a time were talking about:

    There are high energy particles called lambda's that exist only for a mere 1E-10 seconds before bursting forth into a sea of low energy particles. In one theory of how the universe will end, the universe will be ripped apart by the same phantom force purported to be accelerating the expansion of the universe. It is said that this will not occur for another 1E19 seconds, or about 300 billion years. What if the universe were really just an unstable lambda particle in some higher universe? What takes 300 billion years for us, would merely be an instant of 1E-10 seconds for observers in this "2nd Order Universe". This 2nd Order universe may then merely be an unstable lambda in a 3rd Order Universe, and so on. Just imagine the deep time that must pass for a 3rd order universe to perish! By the time 10^(10^3000) years had passed a (1E2998)th order universe would have perished!!

    Mind boggling. Even this analogy fails to express the deepness of such time, as the number 1E2998 is already to large for us to contemplate. If God passed the eternity before creation by idly counting this is what it would be like!

    It's worth stopping to realize that Bowers system enables us more room for counting than we'd ever need, even to count all the particles in the universe! And that is really a great big understatement. One thing that we are eventually going to have to consider is the fact that almost all the large numbers we will consider are more than the number of particles in the universe. After awhile this becomes an inadequate comparison. More apt would be to say that the number is so large that it would provide a name for every number from 1 to the number of particles in the observable universe raised to its own power! That's the terms we have to start thinking in because "reality" as we know it is quickly slipping behind us, and no comparison to such things can really do these numbers justice.

    And yet, ... we still have two more Tiers to go! Let's now head to Tier 3!!

The 3rd Tier Intermediates

    For the 1000th prefix Bowers uses killo, to form killillion (note the use of a double "L", instead of using kilo), the smallest Tier 3 number. To continue on the the 3rd Tier, Bowers begins to use the large scale prefixes. These would be, mega, giga, tera, peta, exa, zetta, and yotta. From these he forms megillion, gigillion, terillion, petillion, exillion, zettillion, and yottillion, by dropping "a" and adding -illion.
   
    In theory these 3rd Tier roots can be used to separate 2nd Tier roots. Beginning to notice a pattern? Unfortunately we hit a bit of a snag at this point. Why? Because we need to find a way to name the 1001st prefix, the 1002nd prefix, and so on in order to continue.

    No big deal, you say. Just take the names from the table. The 1001st prefix would form killo-millillion, the 1002nd prefix would form killo-micrillion ... but wait. Killo-millillion would actually be 1E(3E3000+3003) not 1E(3E3003+3), and killo-micrillion would actually be 1E(3E3000+3,000,003) not 1E(3E3006+3). Although counter-intuitive, these numbers are much much smaller than their expected values. You might argue this is not a problem. We can simply use the greek ones roots, instead of the SI prefixes to avoid confusion. So instead we could have killo-meillion, killo-dueillion, killo-trioillion, etc. This works ... until we reach killo-vecillion. Not to mention stuff like killo-icosillion, or killo-trioicosillion, etc. Another interesting result is that while icosohectillion is the 120th prefix, hecto-icosillion is the 100th plus the 20th, which in this context is not the same thing. Something is seriously wrong!

    How do we get around this problem? Well basically the reason we are having a problem is because we stacked prefixes to describe all the in-betweens. We can not therefore use the same trick to name higher prefixes.

    One way around this that I've devised is to alter the form of the prefixes. When each prefix ends in "o" let it imply the end of a 2nd Class Separator. For example trioicoso, tetrepentaconto, etc. In order to avoid this, we will end a 3rd Class Separator with an "a" when it is not intended as the end of a sequence of modifiers for a 2nd Class Separator. For the Tier 2 roots, they will end in "e" when they are not the end of a Class 2 Separator, and can end in "o" when they are. Thus we use "killa" to continue the 2nd Class Separators. We can remain with the same construction rules, using the SI prefixes first.

    Thus after killo would come:

killamilli, killamicro, killanano, killapico, killafemto, killaatto, killazepto, killayocto, killaxono, killaveco, etc.

    In this way we can continue. Basically we can let killa, mega, giga, tera, peta, exa, zetta, yotta, and so on operate as separators of 2nd Tier roots. When they occur at the end of a Class 2 Separator, they can end in "o" as in killo, mego, gigo, tero, peto, exo, zetto, yotto, etc.

    This also allows us to distinguish killo-millillion as 1E(3E3000+3003) and killamillillion as 1E(3E3003+3) without ambiguity.

    There is also some subtle ambiguities this system also solves. For example what would a killavecohecto-millillion be? Is this the 1120th prefix followed by the first prefix milli? or is it the 1020th prefix followed by the 100th followed by the first? Using the rule of letter changing, such ambiguity can be avoided. A killavecehecto-millillion would be the first case and a killaveco-hecto-millillion would be the second. As far as I can tell these rules help resolve the kinks I've uncovered. Of coarse it's difficult to know whether there are not hidden ambiguities when the number of members can not be inspected directly for comparison.

    To help you understand how these ideas would work in practice I can provide some examples and explanations. Basically just as the root "illion" acts to end a Class 1 separator, "o" acts to end a Class 2 separator. Until "o" occurs, the roots are to be interpreted as part of a Class 2 Separator.

    For example: Consider megamicro-millillion. Since "mega" ends in "a", it is not to be interpreted in isolation. The first root to end in an "o" is "micro". Thus "megamicro" acts as a single unit signifying the 1,000,002nd Class 2 Separator (prefix). This is partly assisted by my use of dashes. The dashes are being used to separate Class 2 Separators. Thus we have two class 2 Separators in this example. We have "megamicro" and we have "milli". So we can say megamicro-millillion is the 1,000,002nd prefix followed by the 1st prefix. It is therefore equivalent to 1E(3E3,000,006+3E3+3).

    Now consider mego-micro-millillion. Here "mego" ends in an "o", and so this terminates the Class 2 Separator. We therefore interpret this as the millionth prefix "mego" followed by the 2nd prefix "micro" followed by the first prefix "milli". Thus mego-micro-millillion as 1E(3E3,000,000+3E6+3E3+3). This number is vastly smaller than the previous example.
 
   We can now continue into the 3rd Tier using the basic rules just proscribed. To make it clear how the rules would be applied to distinguish cases, I'll give some Tier 3 examples in the next table:

Bowers' Tier 3 Intermediates

 Bowers
3rd Tier
Intermediates
Scientific Notation
Half-Scale Notation
 killillion  1E(3E3000+3) H(H(999))
 killo-untillion  1E(3E3000+6) H(H(999)+1)
 killo-duotillion  1E(3E3000+9)  H(H(999)+2)
 killo-tretillion1E(3E3000+12)
H(H(999)+3)
 killo-quadrillion 1E(3E3000+15) H(H(999)+4)
 ...  ... ...
 killo-decillion  1E(3E3000+33) H(H(999)+10)
 killo-centillion  1E(3E3000+303)  H(H(999)+100)
 killo-millillion  1E(3E3000+3003)  H(H(999)+1000)
 killo-milli-untillion  1E(3E3000+3006)  H(H(999)+1001)
killo-micrillion
 1(3E3000+3E6+3) H(H(999)+H(1))
 killo-nanillion  1E(3E3000+3E9+3)  H(H(999)+H(2))
 ...  ...  ...
 killo-enneenneconteennahectillion  1E(3E3000+3E2997+3)  H(H(999)+H(998))
 killo-novemnonagintinongenti-enneenneconteennahectillion  1E(3E3000+2.997E3000+3)  H(H(999)+999*H(998))
 ...  ...  ...
 duokillillion  1E(6E3000+3)  H(2*H(999))
 trekillillion  1E(9E3000+3)  H(3*H(999))
quattourkillillion
 1E(12E3000+3) H(4*H(999))
 quinkillillion  1E(15E3000+3)  H(5*H(999))
 ...  ...  ...
 decikillillion  1E(3E3001+3)  H(10*H(999))
 centikillillion  1E(3E3002+3)  H(100*H(999))
 ...  ...  ...
 novemnonagintinongentikillillion  1E(2.997E3003+3)  H(999*H(999))
 ... ...
 ...
 killamillillion  1E(3E3003+3)  H(H(1000))
 killamilli-untillion  1E(3E3003+6)  H(H(1000)+1)
 killamilli-duotillion  1E(3E3003+9)  H(H(1000)+2)
 ...  ...  ...
 killamilli-decillion  1E(3E3003+33)  H(H(1000)+10)
 killamilli-centillion  1E(3E3003+303)  H(H(1000)+100)
 killamilli-millillion  1E(3E3003+3003)  H(H(1000)+1000)
 killamilli-decimillillion  1E(3E3003+30,003)  H(H(1000)+10,000)
 killamilli-centimillillion  1E(3E3003+300,003)  H(H(1000)+100,000)
 killamilli-micrillion  1E(3E3003+3E6+3)  H(H(1000)+H(1))
 ...  ...  ...
 killamilli-killillion  1E(3E3003+3E3000+3)  H(H(1000)+H(999))
 killamilli-killo-untillion  1E(3E3003+3E3000+6)  H(H(1000)+H(999)+1)
 ...
 ...  ...
 killamilli-duokillillion  1E(3E3003+6E3000+3)  H(H(1000)+2*H(999))
 killamilli-trekillillion  1E(3E3003+9E3000+3)  H(H(1000)+3*H(999))
 killamilli-quattuorkillillion  1E(3E3003+12E3000+3)  H(H(1000)+4*H(999))
 killamilli-quinkillillion  1E(3E3003+15E3000+3)  H(H(1000)+5*H(999))
 ...  ...  ...
 killamilli-decikillillion  1E(3E3003+3E3001+3)  H(H(1000)+10*H(999))
 killamilli-centikillillion  1E(3E3003+3E3002+3)  H(H(1000)+100*H(999))
 ...  ...  ...
 killamilli-novemnonagintinongenti-killillion  1E(3E3003+2.997E3003+3)  H(H(1000)+999*H(999))
 duokillamillillion  1E(6E3003+3)  H(2*H(1000))
...
 ...  ...
trekillamillillion
 1E(9E3003+3)  H(3*H(1000))
 quattuorkillamillillion  1E(12E3003+3)  H(4*H(1000))
 quinkillamillillion  1E(15E3003+3)  H(5*H(1000))
 ...  ...  ...
 decikillamillillion  1E(3E3004+3)  H(10*H(1000))
 centikillamillillion  1E(3E3005+3)  H(100*H(1000))
 ...  ...  ...
 novemnonagintinongenti-killamillillion  1E(2.997E3006+3)  H(999*H(1000))
 ... ...
 ...
 killamicrillion  1E(3E3006+3)  H(H(1001))
 killamicro-untillion  1E(3E3006+6)  H(H(1001)+1)
 ...  ...  ...
 killamicro-killo-micrillion  1E(3E3006+3E3000+3E6+3)  H(H(1001)+H(999)+H(1))
 ...  ...  ...
 killananillion  1E(3E3009+3)  H(H(1002))
 killanano-killo-nanillion  1E(3E3009+3E3000+3E9+3)  H(H(1002)+H(999)+H(2))
 ...  ...  ...
 killapicillion  1E(3E3012+3)  H(H(1003))
 killapico-killo-picillion  1E(3E3012+3E3000+3E12+3)  H(H(1003)+H(999)+H(3))
 ...  ...
 ...
 killafemtillion  1E(3E3015+3)  H(H(1004))
 killafemto-killo-femtillion  1E(3E3015+3E3000+3E15+3)  H(H(1004)+H(999)+H(4))
 ...  ...  ...
 killaattillion 1E(3E3018+3)
 H(H(1005))
 killaatto-killo-attillion  1E(3E3018+3E3000+3E18+3)  H(H(1005)+H(999)+H(5))
 ...  ...  ...
 killazeptillion  1E(3E3021+3)  H(H(1006))
 killazepto-killo-zeptillion  1E(3E3021+3E3000+3E21+3)  H(H(1006)+H(999)+H(6))
 ...  ...  ...
 killayoctillion  1E(3E3024+3)  H(H(1007))
 killayocto-killo-yoctillion  1E(3E3024+3E3000+3E24+3)  H(H(1007)+H(999)+H(7))
 ...  ...  ...
 killaxonillion  1E(3E3027+3)  H(H(1008))
 killaxono-killo-xonillion  1E(3E3027+3E3000+3E27+3)  H(H(1008)+H(999)+H(8))
 ...  ...  ...
 killavecillion  1E(3E3030+3)  H(H(1009))
 ...  ...  ...
 killamecillion  1E(3E3033+3)  H(H(1010))
 ...  ...  ...
 killaduecillion  1E(3E3036+3)  H(H(1011))
 ...  ...  ...
 ...  ...  ...
 killaicosillion  1E(3E3060+3)  H(H(1019))
 killaicoso-killo-icosillion  1E(3E3060+3E3000+3E60+3)  H(H(1019)+H(999)+H(19))
 ...  ...  ...
 killatriacontillion  1E(3E3090+3)  H(H(1029))
 ...  ...  ...
 killatetrecontillion  1E(3E3120+3)  H(H(1039))
 ...  ...  ...
 ...
 ...  ...
 killahectillion  1E(3E3300+3)  H(H(1099))
 killahecto-killo-hectillion  1E(3E3300+3E3000+3E300+3)  H(H(1099)+H(999)+H(99))
 ...  ...  ...
 killamehectillion  1E(3E3303+3)  H(H(1100))
 killaduehectillion  1E(3E3306+3)  H(H(1101))
 ...  ...  ...
 killavecehectillion  1E(3E3330+3)  H(H(1109))
...
 ...  ...
 killaicosehectillion  1E(3E3360+3)  H(H(1119))
 ...  ...  ...
 killatriacontehectillion  1E(3E3390+3)  H(H(1129))
 ...  ...  ...
 ...  ...  ...
 killadohectillion  1E(3E3600+3)  H(H(1199))
 killatriahectillion  1E(3E3900+3)  H(H(1299))
 ...  ...  ...
 killaenneenneconteennahectillion  1E(3E5997+3)  H(H(1998))
 micrekillillion  1E(3E6000+3)  H(H(1999))
 micrekillamillillion  1E(3E6003+3)  H(H(2000))
 micrekillamicrillion  1E(3E6006+3)  H(H(2001))
 micrekillananillion  1E(3E6009+3)  H(H(2002))
 ...  ...  ...
 nanekillillion  1E(3E9000+3)  H(H(2999))
 picekillillion  1E(3E12,000+3)  H(H(3999))
 femtekillillion  1E(3E15,000+3)  H(H(4999))
 attekillillion  1E(3E18,000+3)  H(H(5999))
 zeptekillillion  1E(3E21,000+3)  H(H(6999))
 yoctekillillion  1E(3E24,000+3)  H(H(7999))
 xonekillillion  1E(3E27,000+3)  H(H(8999))
 vecekillillion  1E(3E30,000+3)  H(H(9999))
 mecekillillion  1E(3E33,000+3)  H(H(10,999))
 duecekillillion  1E(3E36,000+3)  H(H(11,999))
 ...  ...  ...
 icosekillillion  1E(3E60,000+3)  H(H(19,999))
 triacontekillillion  1E(3E90,000+3)  H(H(29,999))
 tetrecontekillillion  1E(3E120,000+3)  H(H(39,999))
 ...  ...  ...
 hectekillillion  1E(3E300,000+3)  H(H(99,999))
 ...  ...  ...
 enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E2,999,997+3)  H(H(999,998))
 megillion  1E(3E3,000,000+3) H(H(999,999))
 mego-untillion  1E(3E3,000,000+6)  H(H(999,999)+1)
 ...  ...  ...
mego-millillion
1E(3E3,000,000+3003)
H(H(999,999)+1000)
 mego-micrillion  1E(3E3,000,000+3E6+3)  H(H(999,999)+H(1))
 ...  ...  ...
 mego-killillion  1E(3E3,000,000+3E3000+3)  H(H(999,999)+H(999))
 mego-killo-untillion  1E(3E3,000,000+3E3000+6)  H(H(999,999)+H(999)+1)
 ...  ...  ...
 mego-killo-millillion  1E(3E3,000,000+3E3000+3003)  H(H(999,999)+H(999)+1000)
 mego-killo-micrillion  1E(3E3,000,000+3E3000+3E6+3)  H(H(999,999)+H(999)+H(1))
 mego-killo-nanillion 1E(3E3,000,000+3E3000+3E9+3)
 H(H(999,999)+H(999)+H(2))
 ...  ...  ...
 mego-
killo-enneennecontehectillion
 1E(3E3,000,000+3E3000+
...
3E2997+3)
 H(H(999,999)+H(999)+
...
H(998))
 mego-micrekillillion  1E(3E3,000,000+3E6000+3)  H(H(999,999)+H(1999))
 ...  ...  ...
 mego-nanekillillion  1E(3E3,000,000+3E9000+3)  H(H(999,999)+H(2999))
 mego-picekillillion  1E(3E3,000,000+3E12,000+3)  H(H(999,999)+H(3999))
 mego-femtekillillion  1E(3E3,000,000+3E15,000+3)  H(H(999,999)+H(4999))
 mego-attekillillion  1E(3E3,000,000+3E18,000+3)  H(H(999,999)+H(5999))
 mego-zeptekillillion  1E(3E3,000,000+3E21,000+3)  H(H(999,999)+H(6999))
 mego-yoctekillillion  1E(3E3,000,000+3E24,000+3)  H(H(999,999)+H(7999))
 ...  ...  ...
 mego-
enneenneconteennahectekillillion
 1E(3E3,000,000+3E2,997,000+3)  H(H(999,999)+H(998,999))
 mego-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E3,000,000+3E2,999,997+3)  H(H(999,999)+H(999,998))
 ...  ... ...
 duomegillion  1E(6E3,000,000+3)  H(H(1,999,999))
 tremegillion  1E(9E3,000,000+3)  H(H(2,999,999))
 quattuormegillion  1E(12E3,000,000+3)  H(H(3,999,999))
 quinmegillion  1E(15E3,000,000+3)  H(H(4,999,999))
 ... ...
 ...
 novemnonagintinongenti-
megillion
 1E(2.997E3,000,003+3)  H(H(998,999,999))
...
 ...  ...
 megamillillion  1E(3E3,000,003+3)  H(H(1,000,000))
 megamicrillion  1E(3E3,000,006+3)  H(H(1,000,001))
 ...  ...  ...
 megakillillion  1E(3E3,003,000+3)  H(H(1,000,999))
 megakillo-untillion  1E(3E3,003,000+6)  H(H(1,000,999)+1)
 ...  ...  ...
 megakillo-millillion 1E(3E3,003,000+3003)
 H(H(1,000,999)+1000)
 megakillo-micrillion  1E(3E3,003,000+3E6+3)  H(H(1,000,999)+H(1))
 megakillo-nanillion  1E(3E3,003,000+3E9+3)  H(H(1,000,999)+H(2))
 ...  ...  ...
 megakillo-enneennecontehectillion  1E(3E3,003,000+3E2997+3)  H(H(1,000,999)+H(998))
 ...  ...  ...
 megakillamillillion  1E(3E3,003,003+3)  H(H(1,001,000))
 megakillamicrillion  1E(3E3,003,006+3)  H(H(1,001,001))
 megakillananillion  1E(3E3,003,009+3)  H(H(1,001,002))
 ...  ...  ...
 megakilla-enneenneconteennahectillion  1E(3E3,005,997+3)  H(H(1,001,998))
megamicrekillillion
 1E(3E3,006,000+3)  H(H(1,001,999))
 megamicrekillamillillion  1E(3E3,006,003+3)  H(H(1,002,000))
 megamicrekillamicrillion  1E(3E3,006,006+3)  H(H(1,002,001))
 ...  ...  ...
 megananekillillion  1E(3E3,009,000+3)  H(H(1,002,999))
 megapicekillillion  1E(3E3,012,000+3)  H(H(1,003,999))
 megafemtekillillion  1E(3E3,015,000+3)  H(H(1,004,999))
 megaattekillillion  1E(3E3,018,000+3)  H(H(1,005,999))
 megazeptekillillion  1E(3E3,021,000+3)  H(H(1,006,999))
 megayoctekillillion  1E(3E3,024,000+3)  H(H(1,007,999))
 ...  ...  ...
 mega-
enneenneconteennahectekillillion
 1E(3E5,997,000+3)  H(H(1,998,999))
 mega-
enneenneconteennahectekilla-
enneennecontehectillion
 1E(3E5,999,997+3)  H(H(1,999,998))
 micremegillion  1E(3E6,000,000+3)  H(H(1,999,999))
 ...  ...  ...
 nanemegillion  1E(3E9,000,000+3)  H(H(2,999,999))
 picemegillion  1E(3E12,000,000+3)  H(H(3,999,999))
 femtemegillion  1E(3E15,000,000+3)  H(H(4,999,999))
 attemegillion  1E(3E18,000,000+3)  H(H(5,999,999))
 zeptemegillion  1E(3E21,000,000+3)  H(H(6,999,999))
 yoctemegillion  1E(3E24,000,000+3)  H(H(7,999,999))
 ...  ...  ...
 enneenneconteennahectemega-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E2,999,999,997+3)  H(H(999,999,998))
 gigillion  1E(3E(3E9)+3)  H(H(999,999,999))
 gigo-untillion  1E(3E(3E9)+6)  H(H(999,999,999)+1)
 ...  ...  ...
 gigo-millillion  1E(3E(3E9)+3003)  H(H(999,999,999)+1000)
 gigo-micrillion  1E(3E(3E9)+3E6+3)  H(H(999,999,999)+H(1))
 ...  ...  ...
 gigo-killillion  1E(3E(3E9)+3E3000+3)  H(H(999,999,999)+H(999))
 ...  ...  ...
 gigo-megillion  1E(3E(3E9)+3E3,000,000+3)  H(H(999,999,999)+
...
H(999,999))
 ...  ...  ...
 duogigillion  1E(6E(3E9)+3)  H(2*H(999,999,999))
tregigillion
 1E(9E(3E9)+3)  H(3*H(999,999,999))
 quattuorgigillion  1E(12E(3E9)+3)  H(4*H(999,999,999))
 quingigillion  1E(15E(3E9)+3)  H(5*H(999,999,999))
 ...  ...  ...
novemnonagintinongenti-
gigillion
 1E(2.997E(3E9+3)+3)  H(999*H(999,999,999))
 ...  ...  ...
gigamillillion
 1E(3E(3E9+3)+3)  H(H(1,000,000,000))
 gigamicrillion  1E(3E(3E9+6)+3)  H(H(1,000,000,001))
 gigananillion  1E(3E(3E9+9)+3)  H(H(1,000,000,002))
 ...  ...  ...
 gigaenneennecontehectillion  1E(3E(3E9+2997)+3)  H(H(1,000,000,998))
 gigakillillion  1E(3E(3E9+3000)+3)  H(H(1,000,000,999))
 gigakillamillillion  1E(3E(3E9+3003)+3)  H(H(1,000,001,000))
 gigakillamicrillion  1E(3E(3E9+3006)+3)  H(H(1,000,001,001))
 gigakillananillion  1E(3E(3E9+3009)+3)  H(H(1,000,001,002))
 ...  ...  ...
 gigakillaenneennecontehectillion  1E(3E(3E9+5997)+3)  H(H(1,000,001,998))
 gigamicrekillillion  1E(3E(3E9+6000)+3)  H(H(1,000,001,999))
 gigamicrekillamillillion  1E(3E(3E9+6003)+3)  H(H(1,000,002,000))
 ...  ...  ...
 gigananekillillion  1E(3E(3E9+9000)+3)  H(H(1,000,002,999))
 gigapicekillillion  1E(3E(3E9+12,000)+3)  H(H(1,000,003,999))
 gigafemtekillillion  1E(3E(3E9+15,000)+3)  H(H(1,000,004,999))
 gigaattekillillion  1E(3E(3E9+18,000)+3)  H(H(1,000,005,999))
 gigazeptekillillion  1E(3E(3E9+21,000)+3)  H(H(1,000,006,999))
 gigayoctekillillion  1E(3E(3E9+24,000)+3)  H(H(1,000,007,999))
 ...  ...  ...
 giga-
enneenneconteennahectekillillion
 1E(3E(3E9+2,997,000)+3)  H(H(1,000,998,999))
 giga-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(3E9+2,999,997)+3)  H(H(1,000,999,998))
 gigamegillion  1E(3E(3E9+3,000,000)+3)  H(H(1,000,999,999))
 gigamegamillillion  1E(3E(3E9+3,000,003)+3)  H(H(1,001,000,000))
 gigamegamicrillion  1E(3E(3E9+3,000,006)+3)  H(H(1,001,000,001))
 ...  ...  ...
 gigamegakillillion  1E(3E(3E9+3,003,000)+3)  H(H(1,001,000,999))
 ...  ...  ...
 giga-
enneenneconteennahectemega-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(6E9-3)+3)  H(H(1,999,999,998))
 micregigillion  1E(3E(6E9)+3)  H(H(1,999,999,999))
...
 ...  ...
 nanegigillion  1E(3E(9E9)+3)  H(H(2,999,999,999))
 picegigillion  1E(3E(12E9)+3)  H(H(3,999,999,999))
 femtegigillion  1E(3E(15E9)+3)  H(H(4,999,999,999))
 attegigillion  1E(3E(18E9)+3)  H(H(5,999,999,999))
zeptegigillion  1E(3E(21E9)+3)  H(H(6,999,999,999))
yoctegigillion
 1E(3E(24E9)+3)  H(H(7,999,999,999))
 ...  ...  ...
 enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(3E12-3)+3)  H(H(H(3)-2))
terillion
 1E(3E(3E12)+3)  H(H(H(3)-1))
 tero-untillion 1E(3E(3E12)+6)
 H(H(H(3)-1)+1)
 ...  ...  ...
 tero-millillion  1E(3E(3E12)+3003)  H(H(H(3)-1)+1000)
 tero-micrillion  1E(3E(3E12)+3E6+3)  H(H(H(3)-1)+H(1))
 ...  ...  ...
 tero-killillion  1E(3E(3E12)+3E3000+3)  H(H(H(3)-1)+H(999))
 tero-megillion  1E(3E(3E12)+3E3,000,000+3)  H(H(H(3)-1)+H(999,999))
 tero-gigillion  1E(3E(3E12)+3E(3E9)+3)  H(H(H(3)-1)+H(999,999,999))
 ...  ...  ...
 duoterillion  1E(6E(3E12)+3)  H(2*H(H(3)-1))
 treterillion  1E(9E(3E12)+3)  H(3*H(H(3)-1))
 quattuorterillion  1E(12E(3E12)+3)  H(4*H(H(3)-1))
 ...  ...  ...
 novemnonagintinongentiterillion  1E(2.997E(3E12+3)+3)  H(999*H(H(3)-1))
 ...  ...  ...
 teramillillion  1E(3E(3E12+3)+3)  H(H(H(3)))
 teramicrillion  1E(3E(3E12+6)+3)  H(H(H(3)+1))
 ...  ...  ...
 terakillillion  1E(3E(3E12+3000)+3)  H(H(H(3)+999))
 terakillamillillion  1E(3E(3E12+3003)+3)  H(H(H(3)+1000))
 terakillamicrillion  1E(3E(3E12+3006)+3)  H(H(H(3)+1001))
 ...  ...  ...
 teramicrekillillion  1E(3E(3E12+6000)+3)  H(H(H(3)+1999))
 terananekillillion  1E(3E(3E12+9000)+3)  H(H(H(3)+2999))
 ...  ...  ...
 teramegillion  1E(3E(3E12+3,000,000)+3)  H(H(H(3)+999,999))
 ...  ...  ...
 teragigillion  1E(3E(3E12+3E9)+3)  H(H(H(3)+999,999,999))
 teragigamegakillillion  1E(3E(3E12+3E9+3,003,000)+3)  H(H(H(3)+H(2)+H(1)+999))
 tera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(6E12-3)+3)  H(H(2*H(3)-2))
 micreterillion  1E(3E(6E12)+3)  H(H(2*H(3)-1))
 naneterillion  1E(3E(9E12)+3)  H(H(3*H(3)-1))
 ...  ...  ...
 enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(3E15-3)+3)  H(H(H(4)-2))
petillion
 1E(3E(3E15)+3)  H(H(H(4)-1))
 peto-untillion 1E(3E(3E15)+6)
 H(H(H(4)-1)+1)
 ...  ...  ...
 peto-millillion  1E(3E(3E15)+3003)  H(H(H(4)-1)+1000)
 peto-micrillion  1E(3E(3E15)+3,000,003)  H(H(H(4)-1)+H(1))
 ...  ...  ...
 peto-killillion  1E(3E(3E15)+3E3000+3)  H(H(H(4)-1)+H(999))
 peto-megillion  1E(3E(3E15)+3E3,000,000+3)  H(H(H(4)-1)+H(999,999))
 peto-gigillion  1E(3E(3E15)+3E(3E9)+3)  H(H(H(4)-1)+H(999,999,999))
 peto-terillion  1E(3E(3E15)+3E(3E12)+3)  H(H(H(4)-1)+H(H(3)-1))
 ...  ...  ...
 duopetillion  1E(6E(3E15)+3)  H(2*H(H(4)-1))
 trepetillion  1E(9E(3E15)+3)  H(3*H(H(4)-1))
 quattuorpetillion  1E(12E(3E15)+3)  H(4*H(H(4)-1))
 ...  ...  ...
 novemnonagintinongentipetillion
 1E(2.997E(3E15+3)+3)  H(999*H(H(4)-1))
 petamillillion  1E(3E(3E15+3)+3)  H(H(H(4)))
 petamilli-untillion  1E(3E(3E15+3)+6)  H(H(H(4))+1)
 ...  ...  ...
 petamicrillion  1E(3E(3E15+6)+3)  H(H(H(4)+1))
 petananillion  1E(3E(3E15+9)+3)  H(H(H(4)+2))
 petapicillion  1E(3E(3E15+12)+3)  H(H(H(4)+3))
 ...  ...  ...
 petakillillion  1E(3E(3E15+3000)+3)  H(H(H(4)+999))
 petakillamillillion  1E(3E(3E15+3003)+3)  H(H(H(4)+1000))
 ...  ...  ...
 petamicrekillillion  1E(3E(3E15+6000)+3)  H(H(H(4)+1999))
 petananekillillion  1E(3E(3E15+9000)+3)  H(H(H(4)+2999))
 ...  ...  ...
 petamegillion  1E(3E(3E15+3,000,000)+3)  H(H(H(4)+999,999))
 petagigillion  1E(3E(3E15+3E9)+3)  H(H(H(4)+999,999,999))
 petaterillion  1E(3E(3E15+3E12)+3)  H(H(H(4)+H(3)-1))
 ...  ...  ...
 micrepetillion  1E(3E(6E15)+3)  H(H(2*H(4)-1))
 nanepetillion  1E(3E(9E15)+3)  H(H(3*H(4)-1))
 enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(3E18-3)+3)  H(H(H(5)-2))
 exillion  1E(3E(3E18)+3)  H(H(H(5)-1))
 exo-untillion  1E(3E(3E18)+6)  H(H(H(5)-1)+1)
 ...  ...  ...
 exo-millillion  1E(3E(3E18)+3003)  H(H(H(5)-1)+1000)
 exo-micrillion  1E(3E(3E18)+3,000,003)  H(H(H(5)-1)+H(1))
 ...  ...  ...
 exo-killillion  1E(3E(3E18)+3E3000+3)  H(H(H(5)-1)+H(999))
 exo-megillion  1E(3E(3E18)+3E3,000,000+3)  H(H(H(5)-1)+H(999,999))
 exo-gigillion  1E(3E(3E18)+3E(3E9)+3)  H(H(H(5)-1)+H(999,999,999))
 exo-terillion  1E(3E(3E18)+3E(3E12)+3)  H(H(H(5)-1)+H(H(3)-1))
 exo-petillion  1E(3E(3E18)+3E(3E15)+3)  H(H(H(5)-1)+H(H(4)-1))
 ...  ...  ...
 duoexillion  1E(6E(3E18)+3)  H(2*H(H(5)-1))
 treexillion  1E(9E(3E18)+3)  H(3*H(H(5)-1))
 quattuorexillion  1E(12E(3E18)+3)  H(4*H(H(5)-1))
 ...  ...  ...
 novemnonagintinongentiexillion  1E(2.997E(3E18+3)+3)  H(999*H(H(5)-1))
 examillillion  1E(3E(3E18+3)+3)  H(H(H(5)))
 examicrillion  1E(3E(3E18+6)+3)  H(H(H(5)+1))
 exananillion  1E(3E(3E18+9)+3)  H(H(H(5)+2))
 ...  ...  ...
 exaenneenneconteennahectillion  1E(3E(3E18+2997)+3)  H(H(H(5)+998))
 exakillillion  1E(3E(3E18+3000)+3)  H(H(H(5)+999))
 exakillamillillion  1E(3E(3E18+3003)+3)  H(H(H(5)+1000))
 exakillamicrillion  1E(3E(3E18+3006)+3)  H(H(H(5)+1001))
 ...  ...  ...
 examicrekillillion  1E(3E(3E18+6000)+3)  H(H(H(5)+1999))
 exananekillillion  1E(3E(3E18+9000)+3)  H(H(H(5)+2999))
 ...  ...  ...
 exa-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(3E18+2,999,997)+3)  H(H(H(5)+999,998))
 examegillion  1E(3E(3E18+3,000,000)+3)  H(H(H(5)+999,999))
 ...  ...  ...
 exagigillion  1E(3E(3E18+3E9)+3)  H(H(H(5)+999,999,999))
 exaterillion  1E(3E(3E18+3E12)+3)  H(H(H(5)+H(3)-1))
 exapetillion  1E(3E(3E18+3E15)+3)  H(H(H(5)+H(4)-1))
 exa-
enneenneconteennahectepetillion
 1E(3E(5.997E18)+3)  H(H(H(5)+999*H(4)-1))
 micreexillion  1E(3E(6E18)+3)  H(H(2*H(5)-1))
 ...  ...  ...
 naneexillion  1E(3E(9E18)+3)  H(H(3*H(5)-1))
 piceexillion  1E(3E(12E18)+3)  H(H(4*H(5)-1))
 femteexillion  1E(3E(15E18)+3)  H(H(5*H(5)-1))
 ...  ...  ...
 enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(3E21-3)+3)  H(H(H(6)-2))
zettillion
 1E(3E(3E21)+3) H(H(H(6)-1))
 zetto-untillion  1E(3E(3E21)+6)  H(H(H(6)-1)+1)
 ...  ...  ...
 zetto-millillion  1E(3E(3E21)+3003)  H(H(H(6)-1)+1000)
 zetto-micrillion 1E(3E(3E21)+3,000,003)
 H(H(H(6)-1)+H(1))
 ...  ...  ...
 zetto-killillion  1E(3E(3E21)+3E3000+3)  H(H(H(6)-1)+H(999))
 zetto-megillion  1E(3E(3E21)+3E3,000,000+3)  H(H(H(6)-1)+H(999,999))
 zetto-gigillion  1E(3E(3E21)+3E(3E9)+3)  H(H(H(6)-1)+H(999,999,999))
 zetto-terillion  1E(3E(3E21)+3E(3E12)+3)  H(H(H(6)-1)+H(H(3)-1))
 zetto-petillion  1E(3E(3E21)+3E(3E15)+3)  H(H(H(6)-1)+H(H(4)-1))
 zetto-exillion  1E(3E(3E21)+3E(3E18)+3)  H(H(H(6)-1)+H(H(5)-1))
 ...  ...  ...
 duozettillion  1E(6E(3E21)+3)  H(2*H(H(6)-1))
 trezettillion  1E(9E(3E21)+3)  H(3*H(H(6)-1))
 quattuorzettillion  1E(12E(3E21)+3)  H(4*H(H(6)-1))
 ...  ...  ...
 novemnonagintinongentizettillion 1E(2.997E(3E21+3)+3)
 H(999*H(H(6)-1))
 zettamillillion  1E(3E(3E21+3)+3)  H(H(H(6)))
 zettamilli-untillion  1E(3E(3E21+3)+6)  H(H(H(6))+1)
 ...  ...  ...
 zettamicrillion  1E(3E(3E21+6)+3)  H(H(H(6)+1))
 zettananillion  1E(3E(3E21+9)+3)  H(H(H(6)+2))
 ...  ...  ...
 zetta-enneenneconteennahectillion  1E(3E(3E21+2997)+3)  H(H(H(6)+998))
 zettakillillion  1E(3E(3E21+3000)+3)  H(H(H(6)+999))
 zettakillamillillion  1E(3E(3E21+3003)+3)  H(H(H(6)+1000))
 ...  ...  ...
 zettamicrekillillion  1E(3E(3E21+6000)+3)  H(H(H(6)+1999))
 zettananekillillion  1E(3E(3E21+9000)+3)  H(H(H(6)+2999))
 ...  ...  ...
 zetta-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(3E21+2,999,997)+3)  H(H(H(6)+999,998))
 zettamegillion  1E(3E(3E21+3,000,000)+3)  H(H(H(6)+999,999))
 ...  ...  ...
 zettagigillion  1E(3E(3E21+3E9)+3)  H(H(H(6)+999,999,999))
 zettaterillion  1E(3E(3E21+3E12)+3)  H(H(H(6)+H(3)-1))
 zettapetillion  1E(3E(3E21+3E15)+3)  H(H(H(6)+H(4)-1))
 zettaexillion  1E(3E(3E21+3E18)+3)  H(H(H(6)+H(5)-1))
 ...  ...  ...
 zetta-
enneenneconteennahectexillion
 1E(3E(5.997E21)+3)  H(H(H(6)+999*H(5)-1))
 micrezettillion  1E(3E(6E21)+3)  H(H(2*H(6)-1))
 ...  ...  ...
 nanezettillion  1E(3E(9E21)+3)  H(H(3*H(6)-1))
 picezettillion  1E(3E(12E21)+3)  H(H(4*H(6)-1))
femtezettillion
 1E(3E(15E21)+3)  H(H(5*H(6)-1))
attezettillion
 1E(3E(18E21)+3)  H(H(6*H(6)-1))
 zeptezettillion  1E(3E(21E21)+3)  H(H(7*H(6)-1))
 yoctezettillion  1E(3E(24E21)+3)  H(H(8*H(6)-1))
 ...  ...  ...
 enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(3E24-3)+3)  H(H(H(7)-2))
 yottillion  1E(3E(3E24)+3)  H(H(H(7)-1))
 yotto-untillion  1E(3E(3E24)+6)  H(H(H(7)-1)+1)
...  ...  ...
 yotto-millillion  1E(3E(3E24)+3003)  H(H(H(7)-1)+1000)
 yotto-milli-untillion  1E(3E(3E24)+3006)  H(H(H(7)-1)+1001)
 ...  ...  ...
 yotto-duomillillion  1E(3E(3E24)+6003)  H(H(H(7)-1)+2000)
 ...  ...  ...
 yotto-tremillillion  1E(3E(3E24)+9003)  H(H(H(7)-1)+3000)
 yotto-quattuormillillion  1E(3E(3E24)+12,003)  H(H(H(7)-1)+4000)
 ...  ...  ...
yotto-novemnonagintinongentimilli-
novemnonagintinongentillion
 1E(3E(3E24)+3,000,000)  H(H(H(7)-1)+999,999)
 yotto-micrillion  1E(3E(3E24)+3,000,003)  H(H(H(7)-1)+1,000,000)
 yotto-micro-untillion  1E(3E(3E24)+3,000,006)  H(H(H(7)-1)+1,000,001)
 ...  ...  ...
 yotto-duomicrillion
 1E(3E(3E24)+6,000,003)  H(H(H(7)-1)+2,000,000)
 ...  ...  ...
 yotto-tremicrillion  1E(3E(3E24)+9,000,003)  H(H(H(7)-1)+3,000,000)
 yotto-quattuormicrillion  1E(3E(3E24)+12,000,003)  H(H(H(7)-1)+4,000,000)
 ...  ...  ...
 yotto-
novemnonagintinongentimicro-
novemnonagintinongentimilli-
novemnonagintinongentillion
 1E(3E(3E24)+3E9)  H(H(H(7)-1)+999,999,999)
 yotto-nanillion  1E(3E(3E24)+3E9+3)  H(H(H(7)-1)+1,000,000,000)
 ...  ...  ...
 yotto-picillion  1E(3E(3E24)+3E12+3)  H(H(H(7)-1)+H(3))
 yotto-femtillion  1E(3E(3E24)+3E15+3)  H(H(H(7)-1)+H(4))
 yotto-attillion  1E(3E(3E24)+3E18+3)  H(H(H(7)-1)+H(5))
 yotto-zeptillion  1E(3E(3E24)+3E21+3)  H(H(H(7)-1)+H(6))
 yotto-yoctillion  1E(3E(3E24)+3E24+3)  H(H(H(7)-1)+H(7))
...
 ...  ...
 yotto-enneenneconteennahectillion  1E(3E(3E24)+3E2997+3)  H(H(H(7)-1)+H(998))
 yotto-killillion  1E(3E(3E24)+3E3000+3)  H(H(H(7)-1)+H(999))
 yotto-killamillillion  1E(3E(3E24)+3E3003+3)  H(H(H(7)-1)+H(1000))
 yotto-killamicrillion  1E(3E(3E24)+3E3006+3)  H(H(H(7)-1)+H(1001))
 ...  ...  ...
 yotto-killaenneenneconteennahectillion  1E(3E(3E24)+3E5997+3)  H(H(H(7)-1)+H(1998))
 yotto-micrekillillion  1E(3E(3E24)+3E6000+3)  H(H(H(7)-1)+H(1999))
 ...  ...  ...
 yotto-nanekillillion  1E(3E(3E24)+3E9000+3)  H(H(H(7)-1)+H(2999))
 yotto-picekillillion  1E(3E(3E24)+3E12,000+3)  H(H(H(7)-1)+H(3999))
 yotto-femtekillillion  1E(3E(3E24)+3E15,000+3)  H(H(H(7)-1)+H(4999))
 yotto-attekillillion  1E(3E(3E24)+3E18,000+3)  H(H(H(7)-1)+H(5999))
 yotto-zeptekillillion  1E(3E(3E24)+3E21,000+3)  H(H(H(7)-1)+H(6999))
 yotto-yoctekillillion  1E(3E(3E24)+3E24,000+3)  H(H(H(7)-1)+H(7999))
 ...  ...  ...
 yotto-megillion  1E(3E(3E24)+3E3,000,000+3)  H(H(H(7)-1)+H(999,999))
 yotto-gigillion  1E(3E(3E24)+3E(3E9)+3)  H(H(H(7)-1)+H(999,999,999))
 yotto-terillion  1E(3E(3E24)+3E(3E12)+3)  H(H(H(7)-1)+H(H(3)-1))
 yotto-petillion  1E(3E(3E24)+3E(3E15)+3)  H(H(H(7)-1)+H(H(4)-1))
 yotto-exillion  1E(3E(3E24)+3E(3E18)+3)  H(H(H(7)-1)+H(H(5)-1))
 yotto-zettillion  1E(3E(3E24)+3E(3E21)+3)  H(H(H(7)-1)+H(H(6)-1))
 ...  ...  ...
 duoyottillion  1E(6E(3E24)+3)  H(2*H(H(7)-1))
 treyottillion  1E(9E(3E24)+3)  H(3*H(H(7)-1))
 quattuoryottillion  1E(12E(3E24)+3)  H(4*H(H(7)-1))
 ...  ...  ...
novemnonagintinongentiyottillion
 1E(2.997E(3E24+3)+3)  H(999*H(H(7)-1))
 yottamillillion  1E(3E(3E24+3)+3)  H(H(H(7)))
 yottamicrillion  1E(3E(3E24+6)+3)  H(H(H(7)+1))
 yottananillion  1E(3E(3E24+9)+3)  H(H(H(7)+2))
 yottapicillion  1E(3E(3E24+12)+3)  H(H(H(7)+3))
 yottafemtillion  1E(3E(3E24+15)+3)  H(H(H(7)+4))
 yottaattillion  1E(3E(3E24+18)+3)  H(H(H(7)+5))
 yottazeptillion  1E(3E(3E24+21)+3)  H(H(H(7)+6))
 yottayoctillion  1E(3E(3E24+24)+3)  H(H(H(7)+7))
 ...  ...  ...
 yotta-enneenneconteennahectillion  1E(3E(3E24+2997)+3)  H(H(H(7)+998))
 yottakillillion  1E(3E(3E24+3000)+3)  H(H(H(7)+999))
 yottakillamillillion  1E(3E(3E24+3003)+3)  H(H(H(7)+1000))
 yottakillamicrillion  1E(3E(3E24+3006)+3)  H(H(H(7)+1001))
 yottakillananillion  1E(3E(3E24+3009)+3)  H(H(H(7)+1002))
 yottakillapicillion  1E(3E(3E24+3012)+3)  H(H(H(7)+1003))
 yottakillafemtillion  1E(3E(3E24+3015)+3)  H(H(H(7)+1004))
 yottakillaattillion  1E(3E(3E24+3018)+3)  H(H(H(7)+1005))
 yottakillazeptillion  1E(3E(3E24+3021)+3)  H(H(H(7)+1006))
 yottakillayoctillion  1E(3E(3E24+3024)+3)  H(H(H(7)+1007))
 ...  ...  ...
 yottakilla-
enneenneconteennahectillion
 1E(3E(3E24+5997)+3)  H(H(H(7)+1998))
 yottamicrekillillion  1E(3E(3E24+6000)+3)  H(H(H(7)+1999))
 ...  ...  ...
 yottananekillillion  1E(3E(3E24+9000)+3)  H(H(H(7)+2999))
 yottapicekillillion  1E(3E(3E24+12,000)+3)  H(H(H(7)+3999))
 yottafemtekillillion  1E(3E(3E24+15,000)+3)  H(H(H(7)+4999))
 yottaattekillillion  1E(3E(3E24+18,000)+3)  H(H(H(7)+5999))
 yottazeptekillillion  1E(3E(3E24+21,000)+3)  H(H(H(7)+6999))
 yottayoctekillillion  1E(3E(3E24+24,000)+3)  H(H(H(7)+7999))
 ...  ...  ...
 yotta-
enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(3E24+2,999,997)+3)  H(H(H(7)+999,998))
 yottamegillion  1E(3E(3E24+3,000,000)+3)  H(H(H(7)+999,999))
 ...  ...  ...
 yottagigillion  1E(3E(3E24+3E9)+3)  H(H(H(7)+999,999,999))
 yottaterillion  1E(3E(3E24+3E12)+3)  H(H(H(7)+H(H(3)-1))
 yottapetillion  1E(3E(3E24+3E15)+3)  H(H(H(7)+H(H(4)-1))
 yottaexillion  1E(3E(3E24+3E18)+3)  H(H(H(7)+H(H(5)-1))
 yottazettillion  1E(3E(3E24+3E21)+3)  H(H(H(7)+H(H(6)-1))
 ...  ...  ...
 micreyottillion  1E(3E(6E24)+3)  H(H(2*H(7)-1))
 naneyottillion  1E(3E(9E24)+3)  H(H(3*H(7)-1))
 piceyottillion  1E(3E(12E24)+3)  H(H(4*H(7)-1))
 femteyottillion  1E(3E(15E24)+3)  H(H(5*H(7)-1))
 atteyottillion  1E(3E(18E24)+3)  H(H(6*H(7)-1))
 zepteyottillion  1E(3E(21E24)+3)  H(H(7*H(7)-1))
 yocteyottillion  1E(3E(24E24)+3)  H(H(8*H(7)-1))
 ...  ...  ...
 enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
enneenneconteennahectillion
 1E(3E(3E27-3)+3)  H(H(H(8)-2))
 novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
enneenneconteennahecto-

novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
octeenneconteennahecto-
novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
hepteenneconteennahecto-

novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
hexeenneconteennahecto-
novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
penteenneconteennahecto-

novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
tetreenneconteennahecto-

novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
treenneconteennahecto-

novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
dueenneconteennahecto-

novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
meenneconteennahecto-

novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
enneconteennahecto-

novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
enneocteconteennahecto-

novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-enneenneconteennahectekilla-
octeocteconteennahecto-


...

...

...

...

...

...

...

...

...

novemnonagintinongenti-
icoso-
novemnonagintinongenti-
enneco-
novemnonagintinongenti-
octeco-
novemnonagintinongenti-
hepteco-
novemnonagintinongenti-
hexeco-
novemnonagintinongenti-
penteco-
novemnonagintinongenti-
tetreco-
novemnonagintinongenti-
treco-
novemnonagintinongenti-
dueco-
novemnonagintinongenti-
meco-
novemnonagintinongenti-
veco-
novemnonagintinongenti-
xono-
novemnonagintinongenti-
yocto-
novemnonagintinongenti-
zepto-
novemnonagintinongenti-
atto-
novemnonagintinongenti-
femto-
novemnonagintinongenti-
pico-
novemnonagintinongenti-
nano-
novemnonagintinongenti-
micro-
novemnonagintinongenti-
milli-
novemnonagintinongentillion
 1E(3E(3E27)) H(H(H(8)-1)-1)

    The last entry is the largest illion we can name with the official large scale SI prefixes. You can also bet that this name is also so long that no human being will ever say the whole thing. Roughly speaking you need something like an 100 quintillion years to say it. This says nothing of the largest number the we can name so far. To say that number would take 10^(10^19) years to say. To count to it would take something like 10^(10^(10^19)) years! This numbers are not in the least humanly obtainable, and yet the system we are constructed was constructed by us. We can devise a system which can generate more than a googolplex names for numbers, without actually being able to ever construct them all!

    To go further still Bowers continues the large scale SI prefixes, with some prefixes of his own devising. He decides to adapt his polytope suffixes to use as prefixes for his illions. Let's look into how these prefixes work.

    As stated at the beginning of this article, Bowers is best known for his work with polytopes. Polytopes are multi-dimensional analogies of polygons. For our purposes here we can define a n-dimensional polytope as an mathematical object created by connecting polytopes of one less dimension together to enclose an n-dimensional space. The polytopes of one less dimension used to form an n-dimensional polytope are known as the polytopes "cells". "poly" means many, and a Polytope is essentially an object formed from many cells. A polytope is a generic term for objects of any dimension. However, in ordinary mathematics we also have names for polytopes of a given dimension.

    For example polygons , which exist in 2-dimensional space, are made up of 1-dimensional line segments which enclose an area. A polygon can be thought of as a 2-dimensional polytope. You may also have heard of polyhedrons. A polyhedron is a 3-dimensional polytope formed by joining 2-dimensional polygons at their edges to enclose a 3-dimensional space. The name "polyhedron" actually means "many faces", where the "faces" here refer to the cells. The terms polygon and polyhedron have been around for a long time and are officially recognized by the mathematical community. However there is no officially recognized singular name for 4-dimensional polytopes. Professional mathematicians are not particularly hung up on names. They are sometimes referred to in mathematical literature as 4-polytopes. Some names suggested for the 4-dimensional polytopes are polyhedroids or polycells. Norman Johnson, George Olshevsky, and Jonathan Bowers have advocated the term polychoron. "Choron" here refers to "space" in greek. "Polychoron" therefore translates as "many spaces". This makes sense since each cell of a polychoron is a polyhedron enclosing a 3-dimensional "space". The name also follows a similar naming scheme from polygon and polyhedron. I personally like the term polychoron best of the options proposed. The term is not widely used outside the circle of "polychorists" as far as I know. Although both Jonathan Bowers and George Olshevsky are amateur mathematicians, it is significant to note that Norman Johnson is a professional mathematician and has advocated the use of the term polychoron. Much like the names for very large numbers, naming of the polytopes and there various dimensional categories is esoteric subject matter. For this reason we can expect most of these naming conventions to never be officially recognized. However I might make this suggestion: just because certain esoteric terms may never make it into some kind of universal dictionary, its clear that with esoteric subjects there are only a handful of specialists even interested in such matters. Therefore the names and conventions that such specialists can agree upon should be considered canonical within this limited scope. With that in mind we can say that "polychoron" is the official term amongst those who study them most fervently.

 What does any of this have to do with large numbers? Well the roots, -gon, -hedron, and -choron, form a series of suffixes for the polytopes of various dimensions. Now Bowers has studied polytopes beyond the polychorons. He is responsible for providing a great number of short names for all sorts of polytopes. His naming conventions can be thought of as an evolution from the standard way to name polytopes. Usually a greek prefix is attached to the dimensional suffix to form a polytope name. For example a "pentagon" is a 5-sided polygon. A "tetrahedron" is a 4-celled polyhedron. Bowers uses a similar naming convention with polychorons, where a polychoron is an "n-choron". Since Bowers studies polytopes beyond polychorons he naturally needed higher dimensional suffixes. Originally he used the term polytetron for 5-dimensional polytopes. For technical reasons, the using of latin numbers for the dimensional suffix leads to some ambiguity for the names since it clashes with the use of latin prefixes. As Bowers tells it, Wendy Keiger came up with a solution to this dilemma. She came up with the term polyteron from "tera" the large scale prefix for 1E12. We can assume polyteron to mean "many terons" where a teron is merely another term for a polychoron. Wendy Keiger also came up with the following continuation:

polypeton for 6-dimensional polytopes
polyecton for 7-dimensional polytopes
polyzetton for 8-dimensional polytopes
and
polyyotton for 9-dimensional polytopes

    Bowers then took Wendy's suggestion and went on to extend this up to tredecillionth-dimensional polytopes! Yes you read that correctly. He creates something in the way of an extended system for polytope suffixes. Eventually he decided to adapt these suffixes into prefixes for his illion series, discarding his old "english" roots for new non-standard polytope roots. It seems advisable to avoid using "english" roots in an illion series for one simple consideration. If the Tier 0 roots are being named in english it is likely to cause ambiguity if they are also used at any higher Tier.

    Since the polytope suffixes up to polyyottons are simply based off the large scale SI prefixes it means that they needn't replace the use of large prefixes that we used in the construction of the last table. To see what new large scale prefixes we can devise we must refer to Bowers original list of polytope names. The original list can be found at:

http://www.polytope.net/hedrondude/topes.htm

    For convenience here is a similar table. It shows how we can extract prefixes for the third plateau from his polytope names:

 Dimensions  Bowers' Polytope Names
 Non-Standard Prefix
 1 polytelon
 tela
 2  polygon  ga
 3  polyhedron  hedra
 4  polychoron  chora
 5 polyteron
 tera
 6  polypeton  peta
 7  polyecton  ecta
 8  polyzetton  zetta
 9  polyyotton  yotta
 10  polyxennon  xenna
 11  polydakon  daka
 12  polyhendon  henda
 13  polydokon  doka
 14  polytradakon  tradaka
 15  polytedakon  tedaka
 16  polypedakon  pedaka
 17  polyexdakon  exdaka
 18  polyzedakon  zedaka
 19  polyyodakon  yodaka
 20  polynedakon  nedaka
 21  polyicon  ica
 22  polyikenon  ikena
 23  polyicodon  icoda
 24  polyictron  ictra
 25  polyicteron  ictera
 26  polyicpeton  icpeta
 27  polyikecton  ikecta
 28  polyiczeton  iczeta
 29  polyikyoton  icyota
 30 polyicxenon
 icxena
 31  polytracon traca
41  polytecon  teca
51
 polypecon  peca
61  polyexacon  exaca
71  polyzacon  zaca
81
 polyyocon  yoca
91
 polynecon  neca
100
 polynecxenon  necxena
 101  polyhoton hota
 102 polyhotenon
hotena
 103  polyhotodon  hotoda
 104  polyhotron  hotra
 105  polyhoteron  hotera
 106  polyhopeton  hopeta
 107  polyhotecton  hotecta
 108  polyhozeton  hozeta
 109  polyhoyoton  hoyota
 110  polyhoxenon  hoxena
 111  polyhodakon  hodaka
 112  polyhotendon  hotenda
 113  polyhodokon  hodoka
 114  polyhotradakon  hotradaka
 115  polyhotedakon  hotedaka
 116  polyhopedakon  hopedaka
 117  polyhotexdakon  hotexdaka
 118  polyhozedakon  hozedaka
 119  polyhoyodakon  hoyodaka
 120  polyhonedakon  honedaka
 121  polyhoticon  hotica
 131  polyhotracon  hotraca
 141  polyhotecon  hotecon
 151  polyhopecon  hopecon
 161  polyhotexacon  hotexacon
 171  polyhozacon  hozacon
 181  polyhoyocon  hoyocon
 191  polyhonecon  honecon
 201  polydoton  dota
 218
polydozedakon
 dozedaka
 301 polytroton
 trota
 401  polytoton  tota
 501  polypoton  pota
 601  polyexoton  exota
 701  polyzoton  zota
 801  polyyooton  yoota
 901  polynoton  nota
 1000  polynonecxenon  nonecxena

    Although it might be difficult to discern, it seems that Bowers uses the standard order of roots here. That is, hundreds roots, followed by tens and then ones. From this table it is possible to construct a table of 3rd Tier roots. Here they are:

Bowers' Tier 3 Roots

Value
3rd Ones Roots
3rd Tens Roots
3rd Hundreds Roots
 1
killa/hen/ena
 daka/ka  hota/hot/ho
 2  mega/do/da ika/ik/ico/ic
bota/bot/bo
 3  giga/tra traka/trac/tra
 trota/trot/tro
 4  tera/te  teka/tec/te  tota/tot/to
 5  peta/pe  peka/pec/pe  pota/pot/po
 6  exa/ex/ecta  exaka/exac/exa  exota/exot/exo
 7  zetta/ze/zeta  zaka/zac/za  zota/zot/zo
 8  yotta/yo/yota  yoka/yoc/yo  yoota/yoot/yoo
 9  xenna/ne/xena  neka/nec/ne  nota/not/no

    As you can see there are more spellings for each root than for the 1st and 2nd Tier. This is because of the higher level of irregularity. None the less we can still make sense of this with a few rules.

    Firstly, when 3rd roots are combined, the last root can end in "a" to signify it as a 3rd Tier prefix embedded within a 2nd Tier prefix. If it ends in "o" it signifies the end of a 2nd Tier prefix. Notice that for each of the roots, there is a version ending in "a" for cases where it terminates a third Tier prefix. This "a" can be dropped when it is appended to "illion". When a 3rd root is not the end of a third Tier prefix, it can end in another vowel besides "a".

    The finer points are basically issues of spelling. The hundreds root should be the 3rd option if the following root begins with a consonant, and the 2nd option when it ends in a vowel. If the hundreds roots ends a sequence of 3rd roots it must use the first option.

    The tens follow a similar set of rules. Firstly if the tens root has value "1", the ones root must be placed first and the 2nd options should be used only. The 2nd option for "10" should only be used for "12". With these two conditions the teens become: hendaka, doka, tradaka, tedaka, pedaka, exdaka, zedaka, yodaka, and nedaka. This is just as it appears in Bowers polytope suffixes, and his illions.

    For all other values of ten we can use the 3rd option when the following root begins with a consonant, and the 2nd option when the following root begins with a vowel. In these instances the 3rd option for the ones should be used.

    This is somewhat more nuanced than the previous two levels, but it is not beyond our ability to work out the details.

    Let's now look at some 3rd Tier examples. We will now wrap up the 3rd Tier in this table:

More Bowers' Tier 3 Intermediates

 Bowers'
3rd Plateau Intermediates
Scientific Notation
Half-Scale Notation
 xennillion  1E(3E(3E27)+3)  H(H(H(8)-1))
 xenno-untillion  1E(3E(3E27)+6)  H(H(H(8)-1)+1)
 ...  ...  ...
 xenno-novemnonagintinongentillion 1E(3E(3E27)+3000)
H(H(H(8)-1)+999)
 xenno-millillion  1E(3E(3E27)+3003)  H(H(H(8)-1)+1000)
 xenno-milli-untillion  1E(3E(3E27)+3006) H(H(H(8)-1)+1001)
 ...  ...  ...
 xenno-duomillillion  1E(3E(3E27)+6003)  H(H(H(8)-1)+2000)
 xenno-tremillillion  1E(3E(3E27)+9003)  H(H(H(8)-1)+3000)
 ...  ...  ...
 xenno-micrillion  1E(3E(3E27)+3,000,003)  H(H(H(8)-1)+H(1))
 xenno-nanillion  1E(3E(3E27)+3E9+3)  H(H(H(8)-1)+H(2))
 ...  ...  ...
 xenno-killillion  1E(3E(3E27)+3E3000+3)  H(H(H(8)-1)+H(999))
 xenno-megillion  1E(3E(3E27)+3E3,000,000+3)  H(H(H(8)-1)+H(999,999))
 xenno-gigillion  1E(3E(3E27)+3E(3E9)+3)  H(H(H(8)-1)+H(H(2)-1))
 xenno-terillion  1E(3E(3E27)+3E(3E12)+3)  H(H(H(8)-1)+H(H(3)-1))
 xenno-petillion  1E(3E(3E27)+3E(3E15)+3)  H(H(H(8)-1)+H(H(4)-1))
 xenno-exillion  1E(3E(3E27)+3E(3E18)+3)  H(H(H(8)-1)+H(H(5)-1))
 xenno-zettillion  1E(3E(3E27)+3E(3E21)+3)  H(H(H(8)-1)+H(H(6)-1))
 xenno-yottillion  1E(3E(3E27)+3E(3E24)+3)  H(H(H(8)-1)+H(H(7)-1))
 ...  ...  ...
 xenno-micreyottillion  1E(3E(3E27)+3E(6E24)+3)  H(H(H(8)-1)+H(2*H(7)-1))
 xenno-naneyottillion 1E(3E(3E27)+3E(9E24)+3)   H(H(H(8)-1)+H(3*H(7)-1))
 ...  ...  ...
 xenno-
novemnonagintinongenti-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(5.997E(3E27)+3)  H(H(H(8)-1)+999*H(H(8)-2))
 duoxennillion  1E(6E(3E27)+3)  H(2*H(H(8)-1))
 ...  ...  ...
 trexennillion  1E(9E(3E27)+3)  H(3*H(H(8)-1))
 quattuorxennillion  1E(12E(3E27)+3)  H(4*H(H(8)-1))
 ...  ...  ...
 novemnonagintinongentixennillion  1E(2.997E(3E27+3)+3)  H(999*H(H(8)-1))
 xennamillillion  1E(3E(3E27+3)+3)  H(H(H(8)))
 xennamicrillion  1E(3E(3E27+6)+3)  H(H(H(8)+1))
 ...  ...  ...
 xennakillillion  1E(3E(3E27+3000)+3)  H(H(H(8)+999))
 xennamegillion  1E(3E(3E27+3,000,000)+3)  H(H(H(8)+H(1)-1))
 xennagigillion  1E(3E(3E27+3E9)+3)  H(H(H(8)+H(2)-1))
 xennaterillion  1E(3E(3E27+3E12)+3)  H(H(H(8)+H(3)-1))
 xennapetillion  1E(3E(3E27+3E15)+3)  H(H(H(8)+H(4)-1))
 xennaexillion  1E(3E(3E27+3E18)+3)  H(H(H(8)+H(5)-1))
 xennazettillion  1E(3E(3E27+3E21)+3)  H(H(H(8)+H(6)-1))
 xennayottillion  1E(3E(3E27+3E24)+3)  H(H(H(8)+H(7)-1))
 xenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(6E27-3)+3)  H(H(2*H(8)-2))
 micrexennillion  1E(3E(6E27)+3)  H(H(2*H(8)-1))
 nanexennillion  1E(3E(9E27)+3) H(H(3*H(8)-1))
 picexennillion  1E(3E(12E27)+3) H(H(4*H(8)-1))
 femtexennillion  1E(3E(15E27)+3)  H(H(5*H(8)-1))
 attexennillion  1E(3E(18E27)+3)  H(H(6*H(8)-1))
 zeptexennillion  1E(3E(21E27)+3)  H(H(7*H(8)-1))
 yoctexennillion  1E(3E(24E27)+3)  H(H(8*H(8)-1))
 xonexennillion  1E(3E(27E27)+3)  H(H(9*H(8)-1))
 ...  ...  ...
 enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(3E30-3)+3)  H(H(H(9)-2))
 dakillion  1E(3E(3E30)+3)  H(H(H(9)-1))
 dako-untillion  1E(3E(3E30)+6)  H(H(H(9)-1)+1)
 ...  ...  ...
 dako-killillion 1E(3E(3E30)+3E3000+3)
 H(H(H(9)-1)+H(999))
 dako-megillion  1E(3E(3E30)+3E3,000,000+3)  H(H(H(9)-1)+H(H(1)-1))
 dako-gigillion  1E(3E(3E30)+3E(3E9)+3)  H(H(H(9)-1)+H(H(2)-1))
 dako-terillion  1E(3E(3E30)+3E(3E12)+3)  H(H(H(9)-1)+H(H(3)-1))
 dako-petillion  1E(3E(3E30)+3E(3E15)+3)  H(H(H(9)-1)+H(H(4)-1))
 dako-exillion  1E(3E(3E30)+3E(3E18)+3)  H(H(H(9)-1)+H(H(5)-1))
 dako-zettillion  1E(3E(3E30)+3E(3E21)+3)  H(H(H(9)-1)+H(H(6)-1))
 dako-yottillion  1E(3E(3E30)+3E(3E24)+3)  H(H(H(9)-1)+H(H(7)-1))
 dako-xennillion  1E(3E(3E30)+3E(3E27)+3)  H(H(H(9)-1)+H(H(8)-1))
 ... ...
...
 duodakillion  1E(6E(3E30)+3)  H(2*H(H(9)-1))
 tredakillion  1E(9E(3E30)+3)  H(3*H(H(9)-1))
 ...  ...  ...
 novemnonagintinongentidakillion  1E(2.997E(3E30+3)+3)  H(999*H(H(9)-1))
 dakamillillion  1E(3E(3E30+3)+3)  H(H(H(9)))
 ...  ...  ...
 dakamicrillion  1E(3E(3E30+6)+3)  H(H(H(9)+1))
 dakananillion  1E(3E(3E30+9)+3)  H(H(H(9)+2))
 ...  ...  ...
 dakakillillion  1E(3E(3E30+3000)+3) H(H(H(9)+999))
 dakamegillion  1E(3E(3E30+3,000,000)+3)  H(H(H(9)+H(1)-1))
 dakagigillion  1E(3E(3E30+3E9)+3)  H(H(H(9)+H(2)-1))
 dakaterillion  1E(3E(3E30+3E12)+3)  H(H(H(9)+H(3)-1))
 dakapetillion  1E(3E(3E30+3E15)+3)  H(H(H(9)+H(4)-1))
 dakaexillion  1E(3E(3E30+3E18)+3)  H(H(H(9)+H(5)-1))
 dakazettillion  1E(3E(3E30+3E21)+3)  H(H(H(9)+H(6)-1))
 dakayottillion  1E(3E(3E30+3E24)+3)  H(H(H(9)+H(7)-1))
 dakaxennillion  1E(3E(3E30+3E27)+3)  H(H(H(9)+H(8)-1))
 ...  ...  ...
 micredakillion  1E(3E(6E30)+3)  H(H(2*H(9)-1))
 nanedakillion  1E(3E(9E30)+3)  H(H(3*H(9)-1))
 ...  ...  ...
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(3E33-3)+3)  H(H(H(10)-2))
 hendakillion  1E(3E(3E33)+3)  H(H(H(10)-1))
 hendako-untillion 1E(3E(3E33)+6)
 H(H(H(10)-1)+1)
 ...  ...  ...
 hendako-killillion  1E(3E(3E33)+3E3000+3)  H(H(H(10)-1)+H(999))
 ...  ...  ...
 duohendakillion  1E(6E(3E33)+3)  H(2*H(H(10)-1))
 ...  ...  ...
 hendakamillillion  1E(3E(3E33+3)+3)  H(H(H(10)))
 ...  ...  ...
 micrehendakillion  1E(3E(6E33)+3)  H(H(2*H(10)-1))
 ...  ...  ...
 enneenneconteennahectehendaka-
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(3E36-3)+3)  H(H(H(11)-2))
 dokillion  1E(3E(3E36)+3)  H(H(H(11)-1))
 doko-untillion  1E(3E(3E36)+6)  H(H(H(11)-1)+1)
 ...  ...  ...
 doko-killillion  1E(3E(3E36)+3E3000+3)  H(H(H(11)-1)+H(999))
 ...  ...  ...
 duodokillion  1E(6E(3E36)+3)  H(2*H(H(11)-1))
 ...  ...  ...
 dokamillillion  1E(3E(3E36+3)+3)  H(H(H(11)))
 ...  ...  ...
 micredokillion  1E(3E(6E36)+3)  H(H(2*H(11)-1))
 ...  ...  ...
 enneenneconteennahectedoka-
enneenneconteennahectehendaka-
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(3E39-3)+3)  H(H(H(12)-2))
 tradakillion  1E(3E(3E39)+3)  H(H(H(12)-1))
 tradako-untillion  1E(3E(3E39)+6)  H(H(H(12)-1)+1)
 ...  ...  ...
 tradako-killillion  1E(3E(3E39)+3E3000+3)  H(H(H(12)-1)+H(999))
 ...  ...  ...
 duotradakillion  1E(6E(3E39)+3)  H(2*H(H(12)-1))
 tretradakillion  1E(9E(3E39)+3)  H(3*H(H(12)-1))
 ...  ...  ...
 tradakamillillion  1E(3E(3E39+3)+3)  H(H(H(12)))
 ... ...
 ...
 micretradakillion  1E(3E(6E39)+3)  H(H(2*H(12)-1))
 ...  ...  ...
 enneenneconteennahectetradaka-
 enneenneconteennahectedoka-
enneenneconteennahectehendaka-
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(3E42-3)+3)  H(H(H(13)-2))
 tedakillion 1E(3E(3E42)+3)
 H(H(H(13)-1))
 tedako-untillion 1E(3E(3E42)+6)
H(H(H(13)-1)+1)
...
 ...  ...
 tedako-killillion 1E(3E(3E42)+3E3000+3)
H(H(H(13)-1)+H(999))
 tedako-megillion 1E(3E(3E42)+3E3,000,000+3)
H(H(H(13)-1)+H(H(1)-1))
 ... ...
...
 duotedakillion  1E(6E(3E42)+3) H(2*H(H(13)-1))
 tretedakillion 1E(9E(3E42)+3)
H(3*H(H(13)-1))
 ... ...
...
 novemnonagintinongentitedakillion 1E(2.997E(3E42+3)+3)
H(999*H(H(13)-1))
 tedakamillillion 1E(3E(3E42+3)+3)
H(H(H(13)))
 tedakamicrillion 1E(3E(3E42+6)+3)
H(H(H(13)+1))
 ... ...
...
 micretedakillion 1E(3E(6E42)+3)
H(H(2*H(13)-1))
 nanetedakillion 1E(3E(9E42)+3)
H(H(3*H(13)-1))
 ... ...
...
enneennecontehectetedaka- 
enneenneconteennahectetradaka-
 enneenneconteennahectedoka-
enneenneconteennahectehendaka-
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
1E(3E(3E45-3)+3)
H(H(H(14)-2))
 pedakillion 1E(3E(3E45)+3)
H(H(H(14)-1))
 pedako-untillion 1E(3E(3E45)+6)
H(H(H(14)-1)+1)
 ... ...
...
 pedako-killillion  1E(3E(3E45)+3E3000+3) H(H(H(14)-1)+H(999))
 ... ...
...
 duopedakillion 1E(6E(3E45)+3)
H(2*H(H(14)-1))
 ... ...
...
 pedakamillillion 1E(3E(3E45+3)+3)
H(H(H(14)))
 ... ...
...
 micrepedakillion 1E(3E(6E45)+3)
H(H(2*H(14)-1))
 ... ...
...
 enneenneconteennahectepedaka-
enneennecontehectetedaka- 
enneenneconteennahectetradaka-
 enneenneconteennahectedoka-
enneenneconteennahectehendaka-
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(3E48-3)+3) H(H(H(15)-2))
 exdakillion 1E(3E(3E48)+3)
H(H(H(15)-1))
 exdako-untillion 1E(3E(3E48)+6)
H(H(H(15)-1)+1)
 ... ...
...
 duoexdakillion 1E(6E(3E48)+3)
H(2*H(H(15)-1))
 ... ...
...
 exdakamillillion  1E(3E(3E48+3)+3) H(H(H(15)))
 ... ...
...
 micreexdakillion 1E(3E(6E48)+3)
H(H(2*H(15)-1))
 ... ...
...
enneenneconteennahecteexdaka-
enneenneconteennahectepedaka-
enneennecontehectetedaka- 
enneenneconteennahectetradaka-
 enneenneconteennahectedoka-
enneenneconteennahectehendaka-
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
1E(3E(3E51-3)+3)
H(H(H(16)-2))
 zedakillion 1E(3E(3E51)+3)
 H(H(H(16)-1))
zedako-untillion
 1E(3E(3E51)+6)  H(H(H(16)-1)+1)
 ...  ...  ...
 zedakamillillion  1E(3E(3E51+3)+3)  H(H(H(16)))
 ...  ...  ...
 micrezedakillion  1E(3E(6E51)+3)  H(H(2*H(16)-1))
 ...  ...  ...
 enneenneconteennahectezedaka-
enneenneconteennahecteexdaka-
enneenneconteennahectepedaka-
enneennecontehectetedaka- 
enneenneconteennahectetradaka-
 enneenneconteennahectedoka-
enneenneconteennahectehendaka-
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(3E54-3)+3)  H(H(H(17)-2))
 yodakillion  1E(3E(3E54)+3)  H(H(H(17)-1))
 yodako-untillion  1E(3E(3E54)+6)  H(H(H(17)-1)+1)
 ...  ...  ...
yodakamillillion
 1E(3E(3E54+3)+3)  H(H(H(17)))
 ...  ... ...
 micreyodakillion  1E(3E(6E54)+3) H(H(2*H(17)-1))
 ...  ... ...
 enneenneconteennahecteyodaka-
 enneenneconteennahectezedaka-
enneenneconteennahecteexdaka-
enneenneconteennahectepedaka-
enneennecontehectetedaka- 
enneenneconteennahectetradaka-
 enneenneconteennahectedoka-
enneenneconteennahectehendaka-
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(3E57-3)+3) H(H(H(18)-2))
 nedakillion  1E(3E(3E57)+3) H(H(H(18)-1))
 nedako-untillion  1E(3E(3E57)+6) H(H(H(18)-1)+1)
 ...  ... ...
 nedakamillillion  1E(3E(3E57+3)+3) H(H(H(18)))
 ...  ... ...
 enneenneconteennahectenedaka-
enneenneconteennahecteyodaka-
 enneenneconteennahectezedaka-
enneenneconteennahecteexdaka-
enneenneconteennahectepedaka-
enneennecontehectetedaka- 
enneenneconteennahectetradaka-
 enneenneconteennahectedoka-
enneenneconteennahectehendaka-
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(3E60-3)+3) H(H(H(19)-2))
 ikillion 1E(3E(3E60)+3)
 H(H(H(19)-1))
 iko-untillion  1E(3E(3E60)+6)  H(H(H(19)-1)+1)
 ...  ...  ...
 ikamillillion  1E(3E(3E60+3)+3)  H(H(H(19)))
 ...  ...  ...
 ikakillillion  1E(3E(3E60+3000)+3) H(H(H(19)+999))
 ikamegillion  1E(3E(3E60+3,000,000)+3)  H(H(H(19)+H(1)-1))
 ikagigillion  1E(3E(3E60+3E9)+3)  H(H(H(19)+H(2)-1))
 ikaterillion  1E(3E(3E60+3E12)+3)  H(H(H(19)+H(3)-1))
 ikapetillion  1E(3E(3E60+3E15)+3)  H(H(H(19)+H(4)-1))
 ikaexillion  1E(3E(3E60+3E18)+3)  H(H(H(19)+H(5)-1))
 ikazettillion  1E(3E(3E60+3E21)+3)  H(H(H(19)+H(6)-1))
 ikayottillion  1E(3E(3E60+3E24)+3)  H(H(H(19)+H(7)-1))
 ikaxennillion  1E(3E(3E60+3E27)+3)  H(H(H(19)+H(8)-1))
 ...  ...  ...
 enneenneconteennahecteika-
enneenneconteennahectenedaka-
enneenneconteennahecteyodaka-
 enneenneconteennahectezedaka-
enneenneconteennahecteexdaka-
enneenneconteennahectepedaka-
enneennecontehectetedaka- 
enneenneconteennahectetradaka-
 enneenneconteennahectedoka-
enneenneconteennahectehendaka-
 enneenneconteennahectedaka-
enneenneconteennahectexenna-
enneenneconteennahecteyotta-
enneenneconteennahectezetta-
enneenneconteennahecteexa-
enneenneconteennahectepeta-
enneenneconteennahectetera-
enneenneconteennahectegiga-
enneenneconteennahectemega-
enneenneconteennahectekilla-enneenneconteennahectillion
 1E(3E(3E63-3)+3)  H(H(H(20)-2))
 ikenillion  1E(3E(3E63)+3)  H(H(H(20)-1))
 ikeno-untillion  1E(3E(3E63)+6)  H(H(H(20)-1)+1)
 ...  ...  ...
 ikenamillillion  1E(3E(3E63+3)+3)  H(H(H(20)))
 ...  ...  ...
 icodillion  1E(3E(3E66)+3)  H(H(H(21)-1))
 icodo-untillion  1E(3E(3E66)+6)  H(H(H(21)-1)+1)
 ...  ...  ...
 icodamillillion  1E(3E(3E66+3)+3)  H(H(H(21)))
 ...  ...  ...
 ictrillion  1E(3E(3E69)+3)  H(H(H(22)-1))
 ictro-untillion  1E(3E(3E69)+6)  H(H(H(22)-1)+1)
 ictramillillion  1E(3E(3E69+3)+3)  H(H(H(22)))
 icterillion 1E(3E(3E72)+3)
H(H(H(23)-1))
 ictero-untillion  1E(3E(3E72)+6)  H(H(H(23)-1)+1)
 icteramillillion  1E(3E(3E72+3)+3)  H(H(H(23)))
 icpetillion  1E(3E(3E75)+3)  H(H(H(24)-1))
 icpeto-untillion  1E(3E(3E75)+6)  H(H(H(24)-1)+1)
 icpetamillillion  1E(3E(3E75+3)+3)  H(H(H(24)))
 ikectillion  1E(3E(3E78)+3)  H(H(H(25)-1))
 ikecto-untillion  1E(3E(3E78)+6)  H(H(H(25)-1)+1)
 ikectamillillion  1E(3E(3E78+3)+3)  H(H(H(25)))
 iczetillion  1E(3E(3E81)+3)  H(H(H(26)-1))
 iczeto-untillion  1E(3E(3E81)+6)  H(H(H(26)-1)+1)
 iczetamillillion  1E(3E(3E81+3)+3)  H(H(H(26)))
 ikyotillion  1E(3E(3E84)+3)  H(H(H(27)-1))
 ikyoto-untillion  1E(3E(3E84)+6)  H(H(H(27)-1)+1)
 ikyotamillillion  1E(3E(3E84+3)+3)  H(H(H(27)))
 icxenillion  1E(3E(3E87)+3)  H(H(H(28)-1))
 icxeno-untillion  1E(3E(3E87)+6)  H(H(H(28)-1)+1)
 icxenamillillion  1E(3E(3E87+3)+3)  H(H(H(28)))
 trakillion  1E(3E(3E90)+3)  H(H(H(29)-1))
 trako-untillion  1E(3E(3E90)+6)  H(H(H(29)-1)+1)
 trakamillillion  1E(3E(3E90+3)+3)  H(H(H(29)))
 ...  ...  ...
 trakakillillion  1E(3E(3E90+3000)+3) H(H(H(29)+999))
 trakamegillion  1E(3E(3E90+3,000,000)+3)  H(H(H(29)+H(1)-1))
 trakagigillion  1E(3E(3E90+3E9)+3)  H(H(H(29)+H(2)-1))
 trakaterillion  1E(3E(3E90+3E12)+3)  H(H(H(29)+H(3)-1))
 trakapetillion  1E(3E(3E90+3E15)+3)  H(H(H(29)+H(4)-1))
 trakaexillion  1E(3E(3E90+3E18)+3)  H(H(H(29)+H(5)-1))
 trakazettillion  1E(3E(3E90+3E21)+3)  H(H(H(29)+H(6)-1))
 trakayottillion  1E(3E(3E90+3E24)+3)  H(H(H(29)+H(7)-1))
 trakaxennillion  1E(3E(3E90+3E27)+3)  H(H(H(29)+H(8)-1))
 ... ...
...
 trakenillion  1E(3E(3E93)+3)  H(H(H(30)-1))
 trakeno-untillion  1E(3E(3E93)+6)  H(H(H(30)-1)+1)
 trakenamillillion  1E(3E(3E93+3)+3)  H(H(H(30)))
 tracodillion  1E(3E(3E96)+3)  H(H(H(31)-1))
tracodo-untillion
 1E(3E(3E96)+6)  H(H(H(31)-1)+1)
 tracodamillillion  1E(3E(3E96+3)+3)  H(H(H(31)))
 tractrillion  1E(3E(3E99)+3)  H(H(H(32)-1))
 tractro-untillion  1E(3E(3E99)+6)  H(H(H(32)-1)+1)
 tractramillillion  1E(3E(3E99+3)+3)  H(H(H(32)))
 tracterillion  1E(3E(3E102)+3)  H(H(H(33)-1))
 tractero-untillion  1E(3E(3E102)+6)  H(H(H(33)-1)+1)
 tracteramillillion  1E(3E(3E102+3)+3)  H(H(H(33)))
 tracpetillion  1E(3E(3E105)+3)  H(H(H(34)-1))
 tracpeto-untillion  1E(3E(3E105)+6)  H(H(H(34)-1)+1)
 tracpetamillillion  1E(3E(3E105+3)+3)  H(H(H(34)))
 trakectillion  1E(3E(3E108)+3)  H(H(H(35)-1))
 trakecto-untillion  1E(3E(3E108)+6)  H(H(H(35)-1)+1)
 trakectamillillion  1E(3E(3E108+3)+3)  H(H(H(35)))
 traczetillion  1E(3E(3E111)+3)  H(H(H(36)-1))
 traczeto-untillion  1E(3E(3E111)+6)  H(H(H(36)-1)+1)
 traczetamillillion  1E(3E(3E111+3)+3)  H(H(H(36)))
trakyotillion
 1E(3E(3E114)+3)  H(H(H(37)-1))
 trakyoto-untillion  1E(3E(3E114)+6)  H(H(H(37)-1)+1)
 trakyotamillillion  1E(3E(3E114+3)+3)  H(H(H(37)))
tracxenillion
 1E(3E(3E117)+3)  H(H(H(38)-1))
 tracxeno-untillion  1E(3E(3E117)+6) H(H(H(38)-1)+1)
 tracxenamillillion  1E(3E(3E117+3)+3)  H(H(H(38))))
 tekillion  1E(3E(3E120)+3)  H(H(H(39)-1))
 teko-untillion 1E(3E(3E120)+6)
 H(H(H(39)-1)+1)
tekamillillion
1E(3E(3E120+3)+3)
 H(H(H(39)))
 ... ...
 ...
 tekakillillion  1E(3E(3E120+3000)+3)  H(H(H(39)+999))
 tekamegillion  1E(3E(3E120+3,000,000)+3)  H(H(H(39)+H(1)-1))
 tekagigillion  1E(3E(3E120+3E9)+3)  H(H(H(39)+H(2)-1))
 tekaterillion  1E(3E(3E120+3E12)+3)  H(H(H(39)+H(3)-1))
 tekapetillion  1E(3E(3E120+3E15)+3)  H(H(H(39)+H(4)-1))
 tekaexillion  1E(3E(3E120+3E18)+3)  H(H(H(39)+H(5)-1))
 tekazettillion  1E(3E(3E120+3E21)+3)  H(H(H(39)+H(6)-1))
 tekayottillion  1E(3E(3E120+3E24)+3)  H(H(H(39)+H(7)-1))
 tekazettillion  1E(3E(3E120+3E27)+3)  H(H(H(39)+H(8)-1))
 ...  ... ...
 tekenillion  1E(3E(3E123)+3)  H(H(H(40)-1))
 tekeno-untillion  1E(3E(3E123)+6)  H(H(H(40)-1)+1)
 tekenamillillion  1E(3E(3E123+3)+3)  H(H(H(40)))
 tecodillion  1E(3E(3E126)+3)  H(H(H(41)-1))
 tecodo-untillion  1E(3E(3E126)+6)  H(H(H(41)-1)+1)
 tecodamillillion  1E(3E(3E126+3)+3)  H(H(H(41)))
 tectrillion  1E(3E(3E129)+3)  H(H(H(42)-1))
 tectro-untillion  1E(3E(3E129)+6)  H(H(H(42)-1)+1)
 tectramillillion  1E(3E(3E129+3)+3)  H(H(H(42)))
 tecterillion  1E(3E(3E132)+3)  H(H(H(43)-1))
 tectero-untillion  1E(3E(3E132)+6)  H(H(H(43)-1)+1)
 tecteramillillion  1E(3E(3E132+3)+3)  H(H(H(43)))
 tecpetillion  1E(3E(3E135)+3)  H(H(H(44)-1))
 tecpeto-untillion  1E(3E(3E135)+6)  H(H(H(44)-1)+1)
 tecpetamillillion  1E(3E(3E135+3)+3)  H(H(H(44)))
 tekectillion  1E(3E(3E138)+3)  H(H(H(45)-1))
 tekecto-untillion  1E(3E(3E138)+6)  H(H(H(45)-1)+1)
 tekectamillillion  1E(3E(3E138+3)+3)  H(H(H(45)))
 teczetillion  1E(3E(3E141)+3)  H(H(H(46)-1))
 teczeto-untillion  1E(3E(3E141)+6)  H(H(H(46)-1)+1)
 teczetamillillion  1E(3E(3E141+3)+3)  H(H(H(46)))
 tekyotillion  1E(3E(3E144)+3)  H(H(H(47)-1))
 tekyoto-untillion  1E(3E(3E144)+6)  H(H(H(47)-1)+1)
 tekyotamillillion  1E(3E(3E144+3)+3)  H(H(H(47)))
 tecxenillion  1E(3E(3E147)+3)  H(H(H(48)-1))
 tecxeno-untillion  1E(3E(3E147)+6)  H(H(H(48)-1)+1)
 tecxenamillillion  1E(3E(3E147+3)+3)  H(H(H(48)))
 pekillion  1E(3E(3E150)+3)  H(H(H(49)-1))
 peko-untillion  1E(3E(3E150)+6)  H(H(H(49)-1)+1)
 pekamillillion  1E(3E(3E150+3)+3)  H(H(H(49)))
 ... ...
...
 pekakillillion  1E(3E(3E150+3000)+3)  H(H(H(49)+999))
 pekamegillion  1E(3E(3E150+3,000,000)+3)  H(H(H(49)+H(1)-1))
 pekagigillion  1E(3E(3E150+3E9)+3)  H(H(H(49)+H(2)-1))
 pekaterillion  1E(3E(3E150+3E12)+3)  H(H(H(49)+H(3)-1))
 pekapetillion  1E(3E(3E150+3E15)+3)  H(H(H(49)+H(4)-1))
 pekaexillion  1E(3E(3E150+3E18)+3)  H(H(H(49)+H(5)-1))
 pekazettillion  1E(3E(3E150+3E21)+3)  H(H(H(49)+H(6)-1))
 pekayottillion  1E(3E(3E150+3E24)+3)  H(H(H(49)+H(7)-1))
 pekaxennillion  1E(3E(3E150+3E27)+3)  H(H(H(49)+H(8)-1))
 ...  ...  ...
 pekenillion  1E(3E(3E153)+3)  H(H(H(50)-1))
 pekeno-untillion  1E(3E(3E153)+6)  H(H(H(50)-1)+1)
 ...  ...  ...
 pecodillion  1E(3E(3E156)+3)  H(H(H(51)-1))
 ...  ...  ...
 pectrillion  1E(3E(3E159)+3)  H(H(H(52)-1))
 ...  ...  ...
 pecterillion  1E(3E(3E162)+3)  H(H(H(53)-1))
 ... ...
 ...
 pecpetillion  1E(3E(3E165)+3) H(H(H(54)-1))
 ...  ...  ...
 pekectillion  1E(3E(3E168)+3)  H(H(H(55)-1))
 ...  ... ...
 peczetillion  1E(3E(3E171)+3)  H(H(H(56)-1))
 ... ...
 ...
 pekyotillion  1E(3E(3E174)+3)  H(H(H(57)-1))
 ...  ...  ...
 pecxenillion  1E(3E(3E177)+3)  H(H(H(58)-1))
 ...  ...  ...
 exakillion  1E(3E(3E180)+3)  H(H(H(59)-1))
 exako-untillion  1E(3E(3E180)+6)  H(H(H(59)-1)+1)
 ...  ...  ...
 exakamillillion  1E(3E(3E180+3)+3)  H(H(H(59)))
 ...  ...  ...
 exakakillillion  1E(3E(3E180+3000)+3) H(H(H(59)+999))
 exakamegillion  1E(3E(3E180+3,000,000)+3)  H(H(H(59)+H(1)-1))
 exakagigillion  1E(3E(3E180+3E9)+3)  H(H(H(59)+H(2)-1))
 exakaterillion  1E(3E(3E180+3E12)+3)  H(H(H(59)+H(3)-1))
 exakapetillion  1E(3E(3E180+3E15)+3)  H(H(H(59)+H(4)-1))
 exakaexillion  1E(3E(3E180+3E18)+3)  H(H(H(59)+H(5)-1))
 exakazettillion  1E(3E(3E180+3E21)+3)  H(H(H(59)+H(6)-1))
 exakayottillion  1E(3E(3E180+3E24)+3)  H(H(H(59)+H(7)-1))
 exakaxennillion  1E(3E(3E180+3E27)+3)  H(H(H(59)+H(8)-1))
 ...  ...  ...
 exakenillion  1E(3E(3E183)+3)  H(H(H(60)-1))
 exacodillion  1E(3E(3E186)+3)  H(H(H(61)-1))
 exactrillion  1E(3E(3E189)+3)  H(H(H(62)-1))
 exacterillion  1E(3E(3E192)+3)  H(H(H(63)-1))
 exacpetillion  1E(3E(3E195)+3)  H(H(H(64)-1))
exakectillion
 1E(3E(3E198)+3)  H(H(H(65)-1))
 exaczetillion  1E(3E(3E201)+3)  H(H(H(66)-1))
 exakyotillion  1E(3E(3E204)+3)  H(H(H(67)-1))
 exacxenillion  1E(3E(3E207)+3)  H(H(H(68)-1))
 zakillion  1E(3E(3E210)+3)  H(H(H(69)-1))
 zako-untillion  1E(3E(3E210)+6)  H(H(H(69)-1)+1)
 ...  ...  ...
 zakamillillion  1E(3E(3E210+3)+3)  H(H(H(69)))
 ...  ...  ...
 zakakillillion 1E(3E(3E210+3000)+3)
 H(H(H(69)+999))
 zakamegillion  1E(3E(3E210+3,000,000)+3)  H(H(H(69)+H(1)-1))
 zakagigillion  1E(3E(3E210+3E9)+3)  H(H(H(69)+H(2)-1))
 zakaterillion  1E(3E(3E210+3E12)+3)  H(H(H(69)+H(3)-1))
 zakapetillion  1E(3E(3E210+3E15)+3)  H(H(H(69)+H(4)-1))
 zakaexillion  1E(3E(3E210+3E18)+3)  H(H(H(69)+H(5)-1))
 zakazettillion  1E(3E(3E210+3E21)+3)  H(H(H(69)+H(6)-1))
 zakayottillion  1E(3E(3E210+3E24)+3)  H(H(H(69)+H(7)-1))
 zakaxennillion  1E(3E(3E210+3E27)+3)  H(H(H(69)+H(8)-1))
 ...  ...  ...
 zakenillion  1E(3E(3E213)+3) H(H(H(70)-1))
 zacodillion  1E(3E(3E216)+3)  H(H(H(71)-1))
 zactrillion  1E(3E(3E219)+3)  H(H(H(72)-1))
 zacterillion  1E(3E(3E222)+3)  H(H(H(73)-1))
 zacpetillion  1E(3E(3E225)+3)  H(H(H(74)-1))
 zakectillion  1E(3E(3E228)+3)  H(H(H(75)-1))
 zaczetillion  1E(3E(3E231)+3)  H(H(H(76)-1))
 zakyotillion  1E(3E(3E234)+3)  H(H(H(77)-1))
 zacxenillion  1E(3E(3E237)+3)  H(H(H(78)-1))
 yokillion  1E(3E(3E240)+3)  H(H(H(79)-1))
yoko-untillion
 1E(3E(3E240)+6)  H(H(H(79)-1)+1)
 ...  ...  ...
 yokamillillion 1E(3E(3E240+3)+3)
 H(H(H(79)))
 ...  ...  ...
 yokakillillion 1E(3E(3E240+3000)+3)
 H(H(H(79)+999))
 yokamegillion  1E(3E(3E240+3,000,000)+3)  H(H(H(79)+H(1)-1))
 yokagigillion  1E(3E(3E240+3E9)+3)  H(H(H(79)+H(2)-1))
 yokaterillion  1E(3E(3E240+3E12)+3)  H(H(H(79)+H(3)-1))
 yokapetillion  1E(3E(3E240+3E15)+3)  H(H(H(79)+H(4)-1))
 yokaexillion  1E(3E(3E240+3E18)+3)  H(H(H(79)+H(5)-1))
 yokazettillion  1E(3E(3E240+3E21)+3)  H(H(H(79)+H(6)-1))
 yokayottillion  1E(3E(3E240+3E24)+3)  H(H(H(79)+H(7)-1))
 yokaxennillion  1E(3E(3E240+3E27)+3)  H(H(H(79)+H(8)-1))
 ...  ...  ...
 yokenillion  1E(3E(3E243)+3)  H(H(H(80)-1))
 yocodillion  1E(3E(3E246)+3)  H(H(H(81)-1))
 yoctrillion  1E(3E(3E249)+3)  H(H(H(82)-1))
 yocterillion  1E(3E(3E252)+3)  H(H(H(83)-1))
 yocpetillion  1E(3E(3E255)+3)  H(H(H(84)-1))
 yokectillion  1E(3E(3E258)+3)  H(H(H(85)-1))
 yoczetillion  1E(3E(3E261)+3)  H(H(H(86)-1))
 yokyotillion  1E(3E(3E264)+3)  H(H(H(87)-1))
 yocxenillion  1E(3E(3E267)+3)  H(H(H(88)-1))
 nekillion  1E(3E(3E270)+3)  H(H(H(89)-1))
 neko-untillion  1E(3E(3E270)+6)  H(H(H(89)-1)+1)
 ...  ...  ...
 nekamillillion  1E(3E(3E270+3)+3) H(H(H(89)))
 ...  ...
 ...
 nekakillillion  1E(3E(3E270+3000)+3)  H(H(H(89)+999))
 nekamegillion  1E(3E(3E270+3,000,000)+3)  H(H(H(89)+H(1)-1))
 nekagigillion  1E(3E(3E270+3E9)+3)  H(H(H(89)+H(2)-1))
 nekaterillion  1E(3E(3E270+3E12)+3)  H(H(H(89)+H(3)-1))
 nekapetillion  1E(3E(3E270+3E15)+3)  H(H(H(89)+H(4)-1))
 nekaexillion  1E(3E(3E270+3E18)+3)  H(H(H(89)+H(5)-1))
 nekazettillion  1E(3E(3E270+3E21)+3)  H(H(H(89)+H(6)-1))
 nekayottillion  1E(3E(3E270+3E24)+3)  H(H(H(89)+H(7)-1))
 nekaxennillion  1E(3E(3E270+3E27)+3)  H(H(H(89)+H(8)-1))
 ...  ...  ...
 nekenillion  1E(3E(3E273)+3)  H(H(H(90)-1))
 necodillion  1E(3E(3E276)+3)  H(H(H(91)-1))
 nectrillion  1E(3E(3E279)+3)  H(H(H(92)-1))
 necterillion  1E(3E(3E282)+3)  H(H(H(93)-1))
 necpetillion  1E(3E(3E285)+3)  H(H(H(94)-1))
 nekectillion  1E(3E(3E288)+3)  H(H(H(95)-1))
 neczetillion  1E(3E(3E291)+3)  H(H(H(96)-1))
 nekyotillion  1E(3E(3E294)+3)  H(H(H(97)-1))
 necxenillion  1E(3E(3E297)+3)  H(H(H(98)-1))
 hotillion  1E(3E(3E300)+3)  H(H(H(99)-1))
 hoto-untillion  1E(3E(3E300)+6)  H(H(H(99)-1)+1)
 ... ...
 ...
 hotamillillion  1E(3E(3E300+3)+3)  H(H(H(99)))
 ...  ...  ...
 hotakillillion 1E(3E(3E300+3000)+3)
H(H(H(99)+999))
 hotamegillion  1E(3E(3E300+3,000,000)+3)  H(H(H(99)+H(1)-1))
 hotagigillion  1E(3E(3E300+3E9)+3)  H(H(H(99)+H(2)-1))
 hotaterillion  1E(3E(3E300+3E12)+3)  H(H(H(99)+H(3)-1))
 hotapetillion  1E(3E(3E300+3E15)+3)  H(H(H(99)+H(4)-1))
 hotaexillion  1E(3E(3E300+3E18)+3)  H(H(H(99)+H(5)-1))
 hotazettillion  1E(3E(3E300+3E21)+3)  H(H(H(99)+H(6)-1))
 hotayottillion  1E(3E(3E300+3E24)+3)  H(H(H(99)+H(7)-1))
 hotaxennillion  1E(3E(3E300+3E27)+3)  H(H(H(99)+H(8)-1))
 ...  ...  ...
 hotenillion  1E(3E(3E303)+3)  H(H(H(100)-1))
 hotodillion  1E(3E(3E306)+3)  H(H(H(101)-1))
 hotrillion  1E(3E(3E309)+3)  H(H(H(102)-1))
 hoterillion  1E(3E(3E312)+3)  H(H(H(103)-1))
 hopetillion  1E(3E(3E315)+3)  H(H(H(104)-1))
 hotectillion  1E(3E(3E318)+3)  H(H(H(105)-1))
 hozetillion  1E(3E(3E321)+3)  H(H(H(106)-1))
 hoyotillion  1E(3E(3E324)+3)  H(H(H(107)-1))
 hoxenillion  1E(3E(3E327)+3)  H(H(H(108)-1))
 hodakillion  1E(3E(3E330)+3)  H(H(H(109)-1))
 hodako-untillion  1E(3E(3E330)+6)  H(H(H(109)-1)+1)
 ...  ...  ...
 hodakamillillion  1E(3E(3E330+3)+3)  H(H(H(109)))
 ...  ...  ...
 hodakakillillion  1E(3E(3E330+3000)+3)  H(H(H(109)+999))
 hodakamegillion  1E(3E(3E330+3,000,000)+3)  H(H(H(109)+H(1)-1))
 hodakagigillion  1E(3E(3E330+3E9)+3)  H(H(H(109)+H(2)-1))
 hodakaterillion  1E(3E(3E330+3E12)+3)  H(H(H(109)+H(3)-1))
 hodakapetillion  1E(3E(3E330+3E15)+3)  H(H(H(109)+H(4)-1))
 hodakaexillion  1E(3E(3E330+3E18)+3)  H(H(H(109)+H(5)-1))
 hodakazettillion  1E(3E(3E330+3E21)+3)  H(H(H(109)+H(6)-1))
 hodakayottillion  1E(3E(3E330+3E24)+3)  H(H(H(109)+H(7)-1))
 hodakaxennillion  1E(3E(3E330+3E27)+3)  H(H(H(109)+H(8)-1))
 ...  ...  ...
 hotendakillion  1E(3E(3E333)+3)  H(H(H(110)-1))
 hodokillion  1E(3E(3E336)+3)  H(H(H(111)-1))
 hotradakillion  1E(3E(3E339)+3)  H(H(H(112)-1))
 hotedakillion  1E(3E(3E342)+3)  H(H(H(113)-1))
 hopedakillion  1E(3E(3E345)+3)  H(H(H(114)-1))
 hotexdakillion  1E(3E(3E348)+3)  H(H(H(115)-1))
 hozedakillion  1E(3E(3E351)+3)  H(H(H(116)-1))
 hoyodakillion  1E(3E(3E354)+3)  H(H(H(117)-1))
 honedakillion  1E(3E(3E357)+3)  H(H(H(118)-1))
 hotikillion  1E(3E(3E360)+3)  H(H(H(119)-1))
 hotikenillion  1E(3E(3E363)+3)  H(H(H(120)-1))
 hoticodillion  1E(3E(3E366)+3)  H(H(H(121)-1))
 hotictrillion  1E(3E(3E369)+3)  H(H(H(122)-1))
 hoticterillion  1E(3E(3E372)+3)  H(H(H(123)-1))
 hoticpetillion  1E(3E(3E375)+3)  H(H(H(124)-1))
 hotikectillion  1E(3E(3E378)+3)  H(H(H(125)-1))
 hoticzetillion  1E(3E(3E381)+3)  H(H(H(126)-1))
 hotikyotillion  1E(3E(3E384)+3)  H(H(H(127)-1))
 hoticxenillion  1E(3E(3E387)+3)  H(H(H(128)-1))
 hotrakillion  1E(3E(3E390)+3)  H(H(H(129)-1))
 hotrakenillion  1E(3E(3E393)+3)  H(H(H(130)-1))
 hotracodillion  1E(3E(3E396)+3)  H(H(H(131)-1))
 hotractrillion  1E(3E(3E399)+3)  H(H(H(132)-1))
 hotracterillion  1E(3E(3E402)+3)  H(H(H(133)-1))
 hotracpetillion  1E(3E(3E405)+3)  H(H(H(134)-1))
 hotrakectillion  1E(3E(3E408)+3)  H(H(H(135)-1))
 hotraczetillion  1E(3E(3E411)+3)  H(H(H(136)-1))
 hotrakyotillion  1E(3E(3E414)+3)  H(H(H(137)-1))
 hotracxenillion  1E(3E(3E417)+3) H(H(H(138)-1))
 hotekillion  1E(3E(3E420)+3)  H(H(H(139)-1))
 hotekenillion  1E(3E(3E423)+3)
 H(H(H(140)-1))
 hotecodillion 1E(3E(3E426)+3)
 H(H(H(141)-1))
 hotectrillion  1E(3E(3E429)+3)  H(H(H(142)-1))
 hotecterillion  1E(3E(3E432)+3)  H(H(H(143)-1))
 hotecpetillion  1E(3E(3E435)+3)  H(H(H(144)-1))
 hotekectillion  1E(3E(3E438)+3)  H(H(H(145)-1))
 hoteczetillion  1E(3E(3E441)+3)  H(H(H(146)-1))
 hotekyotillion  1E(3E(3E444)+3)  H(H(H(147)-1))
 hotecxenillion  1E(3E(3E447)+3)  H(H(H(148)-1))
 hopekillion  1E(3E(3E450)+3) H(H(H(149)-1))
 hopekenillion  1E(3E(3E453)+3)  H(H(H(150)-1))
 hopecodillion  1E(3E(3E456)+3)  H(H(H(151)-1))
 hopectrillion  1E(3E(3E459)+3)  H(H(H(152)-1))
 hopecterillion  1E(3E(3E462)+3)  H(H(H(153)-1))
 hopecpetillion  1E(3E(3E465)+3)  H(H(H(154)-1))
 hopekectillion  1E(3E(3E468)+3)  H(H(H(155)-1))
 hopeczetillion  1E(3E(3E471)+3)  H(H(H(156)-1))
 hopekyotillion  1E(3E(3E474)+3)  H(H(H(157)-1))
 hopecxenillion  1E(3E(3E477)+3)  H(H(H(158)-1))
 hotexakillion  1E(3E(3E480)+3)  H(H(H(159)-1))
 hotexakenillion  1E(3E(3E483)+3)  H(H(H(160)-1))
 hotexacodillion  1E(3E(3E486)+3)  H(H(H(161)-1))
 hotexactrillion  1E(3E(3E489)+3)  H(H(H(162)-1))
 hotexacterillion  1E(3E(3E492)+3)  H(H(H(163)-1))
 hotexacpetillion  1E(3E(3E495)+3)  H(H(H(164)-1))
 hotexakectillion  1E(3E(3E498)+3)  H(H(H(165)-1))
 hotexaczetillion  1E(3E(3E501)+3)  H(H(H(166)-1))
 hotexakyotillion  1E(3E(3E504)+3)  H(H(H(167)-1))
 hotexacxenillion  1E(3E(3E507)+3)  H(H(H(168)-1))
 hozakillion  1E(3E(3E510)+3)  H(H(H(169)-1))
 hozakenillion  1E(3E(3E513)+3)  H(H(H(170)-1))
 hozecodillion  1E(3E(3E516)+3)  H(H(H(171)-1))
 hozectrillion  1E(3E(3E519)+3)  H(H(H(172)-1))
 hozecterillion  1E(3E(3E522)+3)  H(H(H(173)-1))
 hozecpetillion  1E(3E(3E525)+3)  H(H(H(174)-1))
 hozekectillion  1E(3E(3E528)+3)  H(H(H(175)-1))
 hozeczetillion  1E(3E(3E531)+3)  H(H(H(176)-1))
 hozekyotillion  1E(3E(3E534)+3)  H(H(H(177)-1))
 hozecxenillion  1E(3E(3E537)+3)  H(H(H(178)-1))
 hoyokillion  1E(3E(3E540)+3)  H(H(H(179)-1))
 hoyokenillion  1E(3E(3E543)+3)  H(H(H(180)-1))
 hoyocodillion  1E(3E(3E546)+3)  H(H(H(181)-1))
 hoyoctrillion  1E(3E(3E549)+3)  H(H(H(182)-1))
 hoyocterillion  1E(3E(3E552)+3)  H(H(H(183)-1))
 hoyocpetillion  1E(3E(3E555)+3)  H(H(H(184)-1))
 hoyokectillion  1E(3E(3E558)+3)  H(H(H(185)-1))
 hoyoczetillion  1E(3E(3E561)+3)  H(H(H(186)-1))
 hoyokyotillion  1E(3E(3E564)+3)  H(H(H(187)-1))
 hoyocxenillion  1E(3E(3E567)+3)  H(H(H(188)-1))
 honekillion  1E(3E(3E570)+3)  H(H(H(189)-1))
 honekenillion  1E(3E(3E573)+3)  H(H(H(190)-1))
 honecodillion  1E(3E(3E576)+3)  H(H(H(191)-1))
honectrillion
 1E(3E(3E579)+3)  H(H(H(192)-1))
honecterillion
 1E(3E(3E582)+3)  H(H(H(193)-1))
honecpetillion
 1E(3E(3E585)+3)  H(H(H(194)-1))
honekectillion
 1E(3E(3E588)+3)  H(H(H(195)-1))
honeczetillion
 1E(3E(3E591)+3)  H(H(H(196)-1))
honekyotillion
 1E(3E(3E594)+3)  H(H(H(197)-1))
honecxenillion
 1E(3E(3E597)+3)  H(H(H(198)-1))
 botillion  1E(3E(3E600)+3) H(H(H(199)-1))
 botenillion  1E(3E(3E603)+3) H(H(H(200)-1))
 botodillion  1E(3E(3E606)+3)  H(H(H(201)-1))
 botrillion  1E(3E(3E609)+3)  H(H(H(202)-1))
 boterillion  1E(3E(3E612)+3)  H(H(H(203)-1))
 bopetillion  1E(3E(3E615)+3)  H(H(H(204)-1))
 botectillion  1E(3E(3E618)+3)  H(H(H(205)-1))
 bozetillion  1E(3E(3E621)+3)  H(H(H(206)-1))
 boyotillion  1E(3E(3E624)+3)  H(H(H(207)-1))
 boxenillion  1E(3E(3E627)+3)  H(H(H(208)-1))
 bodakillion  1E(3E(3E630)+3)  H(H(H(209)-1))
 botendakillion  1E(3E(3E633)+3)  H(H(H(210)-1))
 bodokillion  1E(3E(3E636)+3)  H(H(H(211)-1))
 botradakillion  1E(3E(3E639)+3)  H(H(H(212)-1))
 botedakillion  1E(3E(3E642)+3)  H(H(H(213)-1))
 bopedakillion  1E(3E(3E645)+3)  H(H(H(214)-1))
 botexadakillion  1E(3E(3E648)+3)  H(H(H(215)-1))
 bozedakillion  1E(3E(3E651)+3)  H(H(H(216)-1))
 boyodakillion  1E(3E(3E654)+3)  H(H(H(217)-1))
 bonedakillion  1E(3E(3E657)+3)  H(H(H(218)-1))
 botikillion  1E(3E(3E660)+3)  H(H(H(219)-1))
 botikenillion  1E(3E(3E663)+3)  H(H(H(220)-1))
 boticodillion  1E(3E(3E666)+3)  H(H(H(221)-1))
 botictrillion  1E(3E(3E669)+3)  H(H(H(222)-1))
 boticterillion  1E(3E(3E672)+3)  H(H(H(223)-1))
 boticpetillion  1E(3E(3E675)+3)  H(H(H(224)-1))
 botikectillion  1E(3E(3E678)+3)  H(H(H(225)-1))
 boticzetillion  1E(3E(3E681)+3)  H(H(H(226)-1))
 botikyotillion  1E(3E(3E684)+3)  H(H(H(227)-1))
 boticxenillion  1E(3E(3E687)+3)  H(H(H(228)-1))
 botrakillion  1E(3E(3E690)+3)  H(H(H(229)-1))
 botrakenillion  1E(3E(3E693)+3)  H(H(H(230)-1))
 botracodillion  1E(3E(3E696)+3)  H(H(H(231)-1))
 botractrillion  1E(3E(3E699)+3)  H(H(H(232)-1))
 botracterillion  1E(3E(3E702)+3)  H(H(H(233)-1))
 ...  ...  ...
 botekillion  1E(3E(3E720)+3)  H(H(H(239)-1))
 botekenillion  1E(3E(3E723)+3)  H(H(H(240)-1))
 botecodillion  1E(3E(3E726)+3)  H(H(H(241)-1))
 botectrillion  1E(3E(3E729)+3)  H(H(H(242)-1))
 ...  ...  ...
 bopekillion  1E(3E(3E750)+3) H(H(H(249)-1))
 bopekenillion  1E(3E(3E753)+3)  H(H(H(250)-1))
 bopecodillion  1E(3E(3E756)+3)  H(H(H(251)-1))
 bopectrillion  1E(3E(3E759)+3)  H(H(H(252)-1))
 ...  ...  ...
 botexakillion  1E(3E(3E780)+3)  H(H(H(259)-1))
 botexakenillion  1E(3E(3E783)+3)
 H(H(H(260)-1))
 botexacodillion  1E(3E(3E786)+3)  H(H(H(261)-1))
 botexactrillion  1E(3E(3E789)+3)  H(H(H(262)-1))
 ...  ...  ...
 bozekillion  1E(3E(3E810)+3)  H(H(H(269)-1))
bozekenillion
 1E(3E(3E813)+3)  H(H(H(270)-1))
 bozecodillion  1E(3E(3E816)+3)  H(H(H(271)-1))
 bozectrillion  1E(3E(3E819)+3)  H(H(H(272)-1))
 ...  ...  ...
 boyokillion  1E(3E(3E840)+3)  H(H(H(279)-1))
 boyokenillion  1E(3E(3E843)+3)  H(H(H(280)-1))
 boyocodillion  1E(3E(3E846)+3)  H(H(H(281)-1))
 boyoctrillion  1E(3E(3E849)+3)  H(H(H(282)-1))
 ...  ...  ...
 bonekillion  1E(3E(3E870)+3)  H(H(H(289)-1))
 bonekenillion  1E(3E(3E873)+3)  H(H(H(290)-1))
 bonecodillion  1E(3E(3E876)+3)  H(H(H(291)-1))
 bonectrillion  1E(3E(3E879)+3)  H(H(H(292)-1))
 ...  ...  ...
 trotillion  1E(3E(3E900)+3)  H(H(H(299)-1))
 trotenillion  1E(3E(3E903)+3)  H(H(H(300)-1))
 trotodillion  1E(3E(3E906)+3)  H(H(H(301)-1))
 trotrillion  1E(3E(3E909)+3)  H(H(H(302)-1))
 troterillion  1E(3E(3E912)+3)  H(H(H(303)-1))
 ...  ...  ...
 trodakillion  1E(3E(3E930)+3)  H(H(H(309)-1))
 trotendakillion  1E(3E(3E933)+3)  H(H(H(310)-1))
 trodokillion  1E(3E(3E936)+3)  H(H(H(311)-1))
 trotradakillion  1E(3E(3E939)+3)  H(H(H(312)-1))
 trotedakillion  1E(3E(3E942)+3)  H(H(H(313)-1))
 ...  ...  ...
 trotikillion  1E(3E(3E960)+3)  H(H(H(319)-1))
 trotikenillion  1E(3E(3E963)+3)  H(H(H(320)-1))
 troticodillion  1E(3E(3E966)+3)  H(H(H(321)-1))
 trotictrillion  1E(3E(3E969)+3)  H(H(H(322)-1))
 ...  ...  ...
 trotrakillion  1E(3E(3E990)+3)  H(H(H(329)-1))
 trotrakenillion  1E(3E(3E993)+3)  H(H(H(330)-1))
 ...  ...  ...
 trotekillion  1E(3E(3E1020)+3)  H(H(H(339)-1))
 ...  ...  ...
 tropekillion  1E(3E(3E1050)+3)  H(H(H(349)-1))
 ...  ...  ...
 trotexakillion  1E(3E(3E1080)+3)  H(H(H(359)-1))
 ...  ...  ...
 trozakillion  1E(3E(3E1110)+3)  H(H(H(369)-1))
 ...  ...  ...
 troyokillion  1E(3E(3E1140)+3)  H(H(H(379)-1))
 ...  ...  ...
 tronekillion  1E(3E(3E1170)+3)  H(H(H(389)-1))
 ... ...
 ...
 totillion  1E(3E(3E1200)+3)  H(H(H(399)-1))
 totenillion  1E(3E(3E1203)+3)  H(H(H(400)-1))
 totodillion  1E(3E(3E1206)+3)  H(H(H(401)-1))
 totrillion  1E(3E(3E1209)+3)  H(H(H(402)-1))
 toterillion  1E(3E(3E1212)+3)  H(H(H(403)-1))
 ...  ...  ...
 todakillion  1E(3E(3E1230)+3)  H(H(H(409)-1))
 totendakillion  1E(3E(3E1233)+3)  H(H(H(410)-1))
 ...  ...  ...
 totikillion  1E(3E(3E1260)+3)  H(H(H(419)-1))
 ...  ...  ...
 totrakillion  1E(3E(3E1290)+3)  H(H(H(429)-1))
 ...  ...  ...
 totekillion  1E(3E(3E1320)+3)  H(H(H(439)-1))
 ...  ...  ...
 topekillion  1E(3E(3E1350)+3)  H(H(H(449)-1))
 ...  ...  ...
 totexakillion  1E(3E(3E1380)+3)  H(H(H(459)-1))
 ...  ...  ...
 tozakillion  1E(3E(3E1410)+3)  H(H(H(469)-1))
...
 ...  ...
 toyokillion  1E(3E(3E1440)+3)  H(H(H(479)-1))
 ...  ...  ...
 tonekillion  1E(3E(3E1470)+3)  H(H(H(489)-1))
 ...  ...  ...
 potillion  1E(3E(3E1500)+3)  H(H(H(499)-1))
 potenillion 1E(3E(3E1503)+3)H(H(H(500)-1))
 potodillion 1E(3E(3E1506)+3) H(H(H(501)-1))
 potrillion 1E(3E(3E1509)+3) H(H(H(502)-1))
 poterillion 1E(3E(3E1512)+3) H(H(H(503)-1))
 popetillion 1E(3E(3E1515)+3) H(H(H(504)-1))
 potectillion 1E(3E(3E1518)+3) H(H(H(505)-1))
 ......
 ...
 podakillion 1E(3E(3E1530)+3) H(H(H(509)-1))
 potendakillion 1E(3E(3E1533)+3) H(H(H(510)-1))
 ... ... ...
potikillion
 1E(3E(3E1560)+3) H(H(H(519)-1))
 potrakillion 1E(3E(3E1590)+3) H(H(H(529)-1))
 potekillion 1E(3E(3E1620)+3) H(H(H(539)-1))
 popekillion 1E(3E(3E1650)+3) H(H(H(549)-1))
 potexakillion 1E(3E(3E1680)+3) H(H(H(559)-1))
 pozakillion 1E(3E(3E1710)+3) H(H(H(569)-1))
 poyokillion 1E(3E(3E1740)+3) H(H(H(579)-1))
 ponekillion 1E(3E(3E1770)+3) H(H(H(589)-1))
 ... ... ...
 exotillion 1E(3E(3E1800)+3) H(H(H(599)-1))
 exotenillion 1E(3E(3E1803)+3) H(H(H(600)-1))
 exotodillion 1E(3E(3E1806)+3) H(H(H(601)-1))
 exotrillion 1E(3E(3E1809)+3)H(H(H(602)-1))
 exoterillion 1E(3E(3E1812)+3) H(H(H(603)-1))
 ... ... ...
 exodakillion 1E(3E(3E1830)+3) H(H(H(609)-1))
 exotendakillion 1E(3E(3E1833)+3) H(H(H(610)-1))
 ......
 ...
 exotikillion 1E(3E(3E1860)+3) H(H(H(619)-1))
 exotrakillion1E(3E(3E1890)+3)
 H(H(H(629)-1))
 exotekillion 1E(3E(3E1920)+3) H(H(H(639)-1))
 exopekillion 1E(3E(3E1950)+3) H(H(H(649)-1))
 exotexakillion 1E(3E(3E1980)+3) H(H(H(659)-1))
 exozakillion 1E(3E(3E2010)+3) H(H(H(669)-1))
 exoyokillion 1E(3E(3E2040)+3) H(H(H(679)-1))
 exonekillion 1E(3E(3E2070)+3) H(H(H(689)-1))
 ... ... ...
 zotillion 1E(3E(3E2100)+3) H(H(H(699)-1))
 zotenillion 1E(3E(3E2103)+3) H(H(H(700)-1))
 zotodillion 1E(3E(3E2106)+3) H(H(H(701)-1))
 zotrillion 1E(3E(3E2109)+3) H(H(H(702)-1))
 zoterillion 1E(3E(3E2112)+3) H(H(H(703)-1))
 ... ... ...
 zodakillion 1E(3E(3E2130)+3) H(H(H(709)-1))
 zotendakillion 1E(3E(3E2133)+3) H(H(H(710)-1))
 ... ... ...
 zotikillion 1E(3E(3E2160)+3) H(H(H(719)-1))
 zotrakillion 1E(3E(3E2190)+3) H(H(H(729)-1))
 zotekillion 1E(3E(3E2220)+3) H(H(H(739)-1))
 zopekillion 1E(3E(3E2250)+3) H(H(H(749)-1))
 zotexakillion 1E(3E(3E2280)+3) H(H(H(759)-1))
 zozakillion 1E(3E(3E2310)+3) H(H(H(769)-1))
 zoyokillion 1E(3E(3E2340)+3) H(H(H(779)-1))
 zonekillion 1E(3E(3E2370)+3) H(H(H(789)-1))
...
 ... ...
 yootillion 1E(3E(3E2400)+3) H(H(H(799)-1))
 yootenillion 1E(3E(3E2403)+3) H(H(H(800)-1))
 yootodillion 1E(3E(3E2406)+3) H(H(H(801)-1))
 yootrillion 1E(3E(3E2409)+3) H(H(H(802)-1))
 yooterillion 1E(3E(3E2412)+3) H(H(H(803)-1))
 ... ... ...
 yoodakillion 1E(3E(3E2430)+3) H(H(H(809)-1))
 yootendakillion 1E(3E(3E2433)+3) H(H(H(810)-1))
 ... ... ...
 yootikillion 1E(3E(3E2460)+3) H(H(H(819)-1))
 yootrakillion 1E(3E(3E2490)+3) H(H(H(829)-1))
 yootekillion 1E(3E(3E2520)+3) H(H(H(839)-1))
 yoopekillion 1E(3E(3E2550)+3) H(H(H(849)-1))
 yootexakillion 1E(3E(3E2580)+3) H(H(H(859)-1))
 yoozakillion 1E(3E(3E2610)+3) H(H(H(869)-1))
 yooyokillion 1E(3E(3E2640)+3) H(H(H(879)-1))
 yoonekillion 1E(3E(3E2670)+3) H(H(H(889)-1))
 ... ... ...
 notillion 1E(3E(3E2700)+3) H(H(H(899)-1))
 notenillion 1E(3E(3E2703)+3) H(H(H(900)-1))
 notodillion 1E(3E(3E2706)+3) H(H(H(901)-1))
 notrillion 1E(3E(3E2709)+3) H(H(H(902)-1))
 noterillion 1E(3E(3E2712)+3) H(H(H(903)-1))
 ... ... ...
 nodakillion 1E(3E(3E2730)+3) H(H(H(909)-1))
 notendakillion 1E(3E(3E2733)+3) H(H(H(910)-1))
 ... ... ...
 notikillion 1E(3E(3E2760)+3) H(H(H(919)-1))
 notrakillion 1E(3E(3E2790)+3) H(H(H(929)-1))
 notekillion 1E(3E(3E2820)+3) H(H(H(939)-1))
 nopekillion 1E(3E(3E2850)+3) H(H(H(949)-1))
 notexakillion 1E(3E(3E2880)+3) H(H(H(959)-1))
 nozakillion 1E(3E(3E2910)+3) H(H(H(969)-1))
 noyokillion 1E(3E(3E2940)+3) H(H(H(979)-1))
 nonekillion 1E(3E(3E2970)+3) H(H(H(989)-1))
 ......
 ...
 nonecxenillion 1E(3E(3E2997)+3) H(H(H(998)-1))

    By now it should be a given that nonecxenillion is not the largest Tier 3 number. However we can say that "nonecxena" forms the largest Class 3 Separator. However we now have 999 Class 3 Separators. By inserting "999" into all of the available Class 2 Groups we can form:

enneennaconteennahectenonecxenaenneennaconteennahectenonekyotaenneennaconteennahecte-noneczetaenneennaconteennahecte nonekecta enneennaconteennahecte nonecpeta enneennaconteennahecte nonectera enneennaconteennahecte nonectra enneennaconteennahecte nonecoda enneennaconteennahecte nonekena enneennaconteennahecte noneka enneennaconteennahecte noyooxena enneennaconteennahecte

... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ...

enneennaconteennahectedakaenneennaconteennahectexennaenneennaconteennahecteyotta- enneennaconteennahectezettaenneennaconteennahecteexaenneennaconteennahectepeta- enneennaconteennahecteteraenneennaconteennahectegigaenneennaconteennahectemega-enneennaconteennahectekillaenneennaconteennahect-illion

    The value of this "number" would be 1E(3E(3E3000-3)+3). This number is so long that it will take about an hour to say. Yet all this number really is, is a huge Class 2 Separator attached to "-illion". How many Class 2 Separators can we now construct? 1E3000-1. Now take each of these constructable Class 2 Separators, and place Class 1 groups between them! That will create the largest illion number we can create within Tier 3:

novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahectenonekyotaenneennaconteennahecte-noneczetaenneennaconteennahecte nonekecta enneennaconteennahecte nonecpeta enneennaconteennahecte nonectera enneennaconteennahecte nonectra enneennaconteennahecte nonecoda enneennaconteennahecte nonekena enneennaconteennahecte noneka enneennaconteennahecte noyooxena enneennaconteennahecte
... ... ... ... ... ... ... ... ... ... ... ...
enneennaconteennahectedakaenneennaconteennahectexennaenneennaconteennahecteyotta- enneennaconteennahectezettaenneennaconteennahecteexaenneennaconteennahectepeta- enneennaconteennahecteteraenneennaconteennahectegigaenneennaconteennahectemega-enneennaconteennahectekillaenneennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahectenonekyotaenneennaconteennahecte-noneczetaenneennaconteennahecte nonekecta enneennaconteennahecte nonecpeta enneennaconteennahecte nonectera enneennaconteennahecte nonectra enneennaconteennahecte nonecoda enneennaconteennahecte nonekena enneennaconteennahecte noneka enneennaconteennahecte noyooxena enneennaconteennahecte
... ... ... ... ... ... ... ... ... ... ... ...
enneennaconteennahectedakaenneennaconteennahectexennaenneennaconteennahecteyotta- enneennaconteennahectezettaenneennaconteennahecteexaenneennaconteennahectepeta- enneennaconteennahecteteraenneennaconteennahectegigaenneennaconteennahectemega-enneennaconteennahectekillaocteennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahectenonekyotaenneennaconteennahecte-noneczetaenneennaconteennahecte nonekecta enneennaconteennahecte nonecpeta enneennaconteennahecte nonectera enneennaconteennahecte nonectra enneennaconteennahecte nonecoda enneennaconteennahecte nonekena enneennaconteennahecte noneka enneennaconteennahecte noyooxena enneennaconteennahecte
... ... ... ... ... ... ... ... ... ... ... ...
enneennaconteennahectedakaenneennaconteennahectexennaenneennaconteennahecteyotta- enneennaconteennahectezettaenneennaconteennahecteexaenneennaconteennahectepeta- enneennaconteennahecteteraenneennaconteennahectegigaenneennaconteennahectemega-enneennaconteennahectekillahepteennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahectenonekyotaenneennaconteennahecte-noneczetaenneennaconteennahecte nonekecta enneennaconteennahecte nonecpeta enneennaconteennahecte nonectera enneennaconteennahecte nonectra enneennaconteennahecte nonecoda enneennaconteennahecte nonekena enneennaconteennahecte noneka enneennaconteennahecte noyooxena enneennaconteennahecte
... ... ... ... ... ... ... ... ... ... ... ...
enneennaconteennahectedakaenneennaconteennahectexennaenneennaconteennahecteyotta- enneennaconteennahectezettaenneennaconteennahecteexaenneennaconteennahectepeta- enneennaconteennahecteteraenneennaconteennahectegigaenneennaconteennahectemega-enneennaconteennahectekillahexeennaconteennahecto-
novemnonagintinongenti-

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

novemnonagintinongenti-veco-novemnonagintinongenti-xono-novemnonagintinongenti-yocto-novemnonagintinongenti-zepto-novemnonagintinongenti-atto-novemnonagintinongenti-femto-novemnonagintinongenti-pico-novemnonagintinongenti-nano-novemnonagintinongenti-micro-novemnonagintinongenti-milli-novemnonagintinongent-illion

    The Class 1 groups have been highlighted in red for constrast. As you can see the structure of the roots is vast, and yet built up from simple counting principles. This number is so vastly huge it will take about 10^3000 years to say, about the same amount of time it would take to count to a millillion. The value of this number would be 1E(3E(3E3000)). Yet even this is not the largest Tier 3 number. This is merely the largest illion. Now take every illion we can construct and place 999 between them all. Thus we would have:

nine hundred ninety nine
novemnonagintinongenti
-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekillaenneennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ...
enneennaconteennahectemega-enneennaconteennahectekillaocteennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekillahepteennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekillahexeennaconteennahecto-
novemnonagintinongenti-

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

novemnonagintinongenti-veco-novemnonagintinongenti-xono-novemnonagintinongenti-yocto-novemnonagintinongenti-zepto-novemnonagintinongenti-atto-novemnonagintinongenti-femto-novemnonagintinongenti-pico-novemnonagintinongenti-nano-novemnonagintinongenti-micro-novemnonagintinongenti-milli-novemnonagintinongent-illion
nine hundred ninety nine
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekillaenneennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ...
enneennaconteennahectemega-enneennaconteennahectekillaocteennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekillahepteennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekilla hexeennaconteennahecto-
novemnonagintinongenti-

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

novemnonagintinongenti-veco-novemnonagintinongenti-xono-novemnonagintinongenti-yocto-novemnonagintinongenti-zepto-novemnonagintinongenti-atto-novemnonagintinongenti-femto-novemnonagintinongenti-pico-novemnonagintinongenti-nano-novemnonagintinongenti-micro-novemnonagintinongenti-milli-octononagintinongent-illion
nine hundred ninety nine
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekillaenneennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ...
enneennaconteennahectemega-enneennaconteennahectekillaocteennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekillahepteennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekilla hexeennaconteennahecto-
novemnonagintinongenti-

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

novemnonagintinongenti-veco-novemnonagintinongenti-xono-novemnonagintinongenti-yocto-novemnonagintinongenti-zepto-novemnonagintinongenti-atto-novemnonagintinongenti-femto-novemnonagintinongenti-pico-novemnonagintinongenti-nano-novemnonagintinongenti-micro-novemnonagintinongenti-milli-septennonagintinongent-illion
nine hundred ninety nine
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekillaenneennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ...
enneennaconteennahectemega-enneennaconteennahectekillaocteennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekillahepteennaconteennahecto-
novemnonagintinongenti-enneennaconteennahectenonecxenaenneennaconteennahecte ... ... ... enneennaconteennahectemega-enneennaconteennahectekilla hexeennaconteennahecto-
novemnonagintinongenti-

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

novemnonagintinongenti-veco-novemnonagintinongenti-xono-novemnonagintinongenti-yocto-novemnonagintinongenti-zepto-novemnonagintinongenti-atto-novemnonagintinongenti-femto-novemnonagintinongenti-pico-novemnonagintinongenti-nano-novemnonagintinongenti-micro-novemnonagintinongenti-milli-sexnonagintinongent-illion
nine hundred ninety nine

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...







... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...

nine hundred ninety nine vigint-illion nine hundred ninety nine novemdec-illion nine hundred ninety nine octodec-illion nine hundred ninety nine septendec-illion nine hundred ninety nine sexdec-illion nine hundred ninety nine quindec-illion nine hundred ninety nine
quattuordec-illion nine hundred ninety nine tredec-illion nine hundred ninety nine
doedec-illion nine hundred ninety nine undec-illion nine hundred ninety nine
dec-illion nine hundred ninety nine non-illion nine hundred ninety nine
oct-illion nine hundred ninety nine sept-illion nine hundred ninety nine
sext-illion nine hundred ninety nine quint-illion nine hundred ninety nine
quadr-illion nine hundred ninety nine tr-illion
nine hundred ninety nine b-illion nine hundred ninety nine m-illion
nine hundred ninety nine
thousand nine hundred ninety nine

    Now THAT is the largest Tier 3 number! The value of that number would be 1E(3E(3E3000)+3)-1. The name of this number is so long that it would take about 10^(10^3000) years just to say. That's about as long as it takes to count to a killillion! Finally to count to this number would take about 10^(10^(10^3000)) years.

    We have now passed up the googol, the googolplex, and even the googolduplex! Do you now see how vast Bowers' system truly is? And yet ... we can understand how to construct it. This is one of those curious paradoxes of large numbers. We can't comprehend their size, but we can comprehend their construction.

    We are now quickly approaching the limit of Bowers' system. Let's now continue on to Tier 4 !!

The 4th Tier Intermediates

    We at last arrive at the 4th and final Tier, the final frontier of counting! (Just a little Bowers' Style humor before we wrap things up). By now the pattern of how to continue should be clear. Every time a Tier ends when all of the roots max out at 999, we can continue by creating a new Tier where we have new roots that act as separators for the roots of one less Tier. To continue therefore we simply need a new root table to start separating Class 3 groups.

    It is here that Bowers' hits a bit of a snag. Having already exhausted latin, greek, and SI prefixes it would seem we have hit a dead end. It is here that Bowers' does something surprising. He opts to invent his own prefixes not based on any pre-existing language or numeric system. To begin he invents a kalillion for the smallest Tier 4 number. "kal" would be the root for the thousandth Class 3 Separator, or the root for the first Class 4 Separator. It is very similar to "kilo" and can be thought of as a variation. The next major milestone on Bowers list is "mejillion". From this we can retract "mej" for the millionth Class 3 Separator. Again this appears as a mere variation on "mega". Next comes a "gijillion", from which he can obtain the billionth Class 3 Separator "gij". This also appears to be a variation on "giga". So what comes next?

    At this point Bowers' breaks the pattern that seems to be established by the first few terms and comes up with a novel continuation. Bowers' creates a series of seemingly unrelated roots inspired by objects and terms in cosmology and astronomy. The very last 11 milestone illions on Bowers list are all related in one way or another to space. With each increase in numerical size Bowers' sensibly chooses an even larger astronomical object from which to derive the necessary root. In the following table, I'll list these milestone illions, their source from Bowers' polytope names, the roots we can derive from them, and where Bowers' drew inspiration to come up with them:

 Bowers' Milestone illion
Bowers' Polytope Name
Root
 Derivation
 astillionpolyaston
ast
asteroid
 lunillionpolylunon
lun
 lunar (moon)
 fermillionpolyfirmon
ferm
terra firma (earth)
 jovillionpolyjovon
jov
jehovan (jupiter)
 solillionpolysolon
sol
solar (sun)
 betillionpolybeton
bet
Betelgeuse
 glocillionpolyglocon
gloc
globular cluster
 gaxillionpolygaxon
gax
galaxy
 supillionpolysupon
sup
super cluster
 versillionpolyverson
vers
universe
 multillionpolymulton
mult
multiverse

    Combined with "kal", "mej", and "gij" we have a total of 14 Class 4 Separators. There aren't any more, so this means Bowers' does not fill out the 4th Tier completely. This is understandable because there isn't any implicit continuation beyond a multillion. What's larger than a multiverse after all, an omniverse? And even then, how far could we continue this until we run out of ideas. Essentially with the 4th Tier Bowers' goes for broke and just takes the astronomical idea to its limit.

    This only leaves the issue of how these roots are to be properly used. Thankfully a simple rule can be used to identify which Class of Separator these roots are terminating. If they are occurring at the end of a Class 2 Separator they can end in "o", as in "kalo", "mejo", "gijo", "asto", "luno", "fermo" etc. If they are occuring at the end of a Class 3 Separator they can end in "a", as in "kala", "meja", "gija", "asta", "luna", "ferma" etc. If they are instead acting as a Class 4 Separator they can simply end in "i", as in "kali", "meji", "giji", "asti", "luni", "fermi" etc. It would seem then that there is no problems left. All we have to do, it would seem, is place Class 3 groups between the Class 4 Separators. Unfortunately Bowers' has one more peculiarity to his system that we must attend to.

    Consider a kalillion. If we were to simply apply the above rules, how would we form the 10,000th Class 3 Separator? We place a Class 3 group equivalent to 10 to the left of "kali". So we would have "dakakalillion". The 100,000th Class 3 Separator would form "hotakalillion". Bowers' does not do this. Instead the 10,000th Class 3 Separator is "dakalillion" and the 100,000th is "hotalillion". We can see these are formed by dropping the first letter from "kali" and adding a Class 3 Group. There is also some finagling with consonants and vowels. For example in "dakalillion", we can think of "daka" being shortened to "dak" before being combined with "ali".

    Is this an isolated case for "kali"? Well we also see a similar approach for the 10 millionth and 100 millionth case. the 10 millionth is "dakejillion" and the 100 millionth is "hotejillion". Could this work for all the Class 4 Separators? Possibly. We can drop the first letter when its a consonant, and we can keep it when its a vowel. Does this settle everything? Well to be absolutely sure let's look over some of the last names on Bowers list. I will list the name, its Class 3 Separator rank, and a possible derivation that will give us a hint at the underlying rules:

 Bowers' Milestone illion
Class 3 Separator Rank
Derivation
 kalillion1000
kali
 dalillion2000
d(a)-(k)ali
 tralillion3000
tr(a)-(k)ali
 talillion4000
t(e)-(k)ali
 palillion5000
p(e)-(k)ali
 exalillion 6000 ex(a)-(k)ali
 zalillion 7000 z(e)-(k)ali
 yalillion 8000 y(o)-(k)ali
 nalillion 9000 n(e)-(k)ali
 dakalillion 10,000 dak(a)-(k)ali
hotalillion
100,000
hot(a)-(k)ali
mejillion
1,000,000
meji
 dakejillion10,000,000
dak(a)-(m)eji
 hotejillion 100,000,000 hot(a)-(m)eji

    This is all we have to go on. None the less, even from this small list of examples a rule can be obtained. We simply drop the last vowel in the Class 3 Group, and follow it with the Class 4 Separator with the leading consonant removed. This practice may even eliminate potential ambiguities, because it strongly implies that the group and its following separator are linked. One ambiguity that could result from my suggestion would be something like meji-daka-kalillion. Is this the 1,000,010th Class 3 Separator followed by the 1000th? or is it the 1,010,000th Class 3 Separator. This could be avoided by altering "daka" as "daki" to imply it is part of a continuing sequence, but Bowers' system works too.

    As far as I can tell this is it. We now have all the rules to complete Bowers' system. If ambiguities should be present, we can change "a"s to "i"s in the Tier 3 roots to imply continuation. We can now construct the Tier 4 root table. This table will not be completely filled out, and we will need to set up a special set of rules for how they work, since they don't follow the usual pattern. None the less here it is:

Bowers' Tier 4 Roots

 Value4th Ones Root
4th Tens Root
4th Hundreds Root
1
kal(o,a,i)/gax(o,a,i)
gloc(o,a,i)
 -
2
 mej(o,a,i)/sup(o,a,i) -
 -
3
 gij(o,a,i)/vers(o,a,i) - -
4
 ast(o,a,i)/mult(o,a,i) - -
5
 lun(o,a,i)/- - -
6
 ferm(o,a,i)/- - -
7
 jov(o,a,i)/- - -
8
 sol(o,a,i)/- - -
9
 bet(o,a,i)/- - -

    The rule here is unusual but simple. If the value is 1~9 just use the 1st option ones root as always. If the value = 10, just use "gloc". For 11~14, don't include a tens root, and simply use the 2nd option ones roots. That's all there is to it.

    So we are now ready to explore the 4th and final Tier. One note of interest before I begin another massive list of examples. The "multillion" is NOT the largest number we can now name, nor is it the largest illion we can form in Bowers' system. We can now actually surpass it. However, Bowers' system doesn't extend all the way to infinity. We are fast approaching a kind of dead end, as you will see shortly. With that in mind, I present the final list of examples before we wrap this up:

 Bowers' 4th Tier Intermediates
Scientific E Notation
Half-Scale Notation
 kalillion 1E(3E(3E3000)+3)H(H(H(999)-1))
 kalo-untillion 1E(3E(3E3000)+6) H(H(H(999)-1)+1)
 kalo-duotillion 1E(3E(3E3000)+9) H(H(H(999)-1)+2)
 kalo-tretillion 1E(3E(3E3000)+12) H(H(H(999)-1)+3)
 kalo-quadrillion 1(3E(3E3000)+15) H(H(H(999)-1)+4)
 ... ... ...
 kalo-novemnonagintinongentillion1E(3E(3E3000)+3000)
H(H(H(999)-1)+999)
 kalo-millillion 1E(3E(3E3000)+3003) H(H(H(999)-1)+1000)
 kalo-milli-untillion 1E(3E(3E3000)+3006) H(H(H(999)-1)+1001)
 ... ... ...
 kalo-milli-novemnonagintinongentillion 1E(3E(3E3000)+6000) H(H(H(999)-1)+1999)
 kalo-duomillillion 1E(3E(3E3000)+6003) H(H(H(999)-1)+2000)
 kalo-duomilli-untillion 1E(3E(3E3000)+6006) H(H(H(999)-1)+2001)
 ... ... ...
 kalo-tremillillion 1E(3E(3E3000)+9003) H(H(H(999)-1)+3000)
 kalo-quattuormillillion 1E(3E(3E3000)+12,003) H(H(H(999)-1)+4000)
 kalo-quinmillillion 1E(3E(3E3000)+15,003) H(H(H(999)-1)+5000)
 ... ... ...
 kalo-
novemnonagintinongentimillillion
 1E(3E(3E3000)+2,997,003) H(H(H(999)-1)+999,000)
 kalo-
novemnonagintinongentimilli-
novemnonagintinongentillion
 1E(3E(3E3000)+3,000,000) H(H(H(999)-1)+999,999)
 kalo-micrillion 1E(3E(3E3000)+3,000,003) H(H(H(999)-1)+H(1))
 kalo-micro-untillion 1E(3E(3E3000)+3,000,006) H(H(H(999)-1)+H(1)+1)
 ... ... ...
 kalo-duomicrillion 1E(3E(3E3000)+6,000,003) H(H(H(999)-1)+2*H(1))
 kalo-duomicro-untillion 1E(3E(3E3000)+6,000,006) H(H(H(999)-1)+2*H(1)+1)
 ... ... ...
 kalo-tremicrillion 1E(3E(3E3000)+9,000,003) H(H(H(999)-1)+3*H(1))
 kalo-quattuormicrillion 1E(3E(3E3000)+12,000,003) H(H(H(999)-1)+4*H(1))
 kalo-quinmicrillion 1E(3E(3E3000)+15,000,003) H(H(H(999)-1)+5*H(1))
 ... ... ...
 kalo-
novemnonagintinongentimicro-
novemnonagintinongentimilli-
novemnonagintinogentillion
 1E(3E(3E3000)+3E9) H(H(H(999)-1)+H(2)-1)
 kalo-nanillion 1E(3E(3E3000)+3E9+3) H(H(H(999)-1)+H(2))
kalo-nano-untillion
 1E(3E(3E3000)+3E9+6) H(H(H(999)-1)+H(2)+1)
 ... ... ...
 kalo-
novemnonagintinongentinano-
novemnonagintinongentimicro-
novemnonagintinongentimilli-
novemnonagintinongentillion
 1E(3E(3E3000)+3E12) H(H(H(999)-1)+H(3)-1)
 kalo-picillion 1E(3E(3E3000)+3E12+3) H(H(H(999)-1)+H(3))
 kalo-pico-untillion 1E(3E(3E3000)+3E12+6) H(H(H(999)-1)+H(3)+1)
 ... ... ...
 kalo-femtillion 1E(3E(3E3000)+3E15+3) H(H(H(999)-1)+H(4))
 kalo-attillion 1E(3E(3E3000)+3E18+3) H(H(H(999)-1)+H(5))
 kalo-zeptillion 1E(3E(3E3000)+3E21+3) H(H(H(999)-1)+H(6))
 kalo-yoctillion 1E(3E(3E3000)+3E24+3) H(H(H(999)-1)+H(7))
 kalo-xonillion 1E(3E(3E3000)+3E27+3) H(H(H(999)-1)+H(8))
 kalo-vecillion 1E(3E(3E3000)+3E30+3) H(H(H(999)-1)+H(9))
 kalo-mecillion 1E(3E(3E3000)+3E33+3) H(H(H(999)-1)+H(10))
 kalo-duecillion 1E(3E(3E3000)+3E36+3) H(H(H(999)-1)+H(11))
 kalo-trecillion 1E(3E(3E3000)+3E39+3) H(H(H(999)-1)+H(12))
 kalo-tetrecillion 1E(3E(3E3000)+3E42+3) H(H(H(999)-1)+H(13))
 kalo-pentecillion 1E(3E(3E3000)+3E45+3) H(H(H(999)-1)+H(14))
 kalo-hexecillion 1E(3E(3E3000)+3E48+3) H(H(H(999)-1)+H(15))
 kalo-heptecillion 1E(3E(3E3000)+3E51+3) H(H(H(999)-1)+H(16))
 kalo-octecillion 1E(3E(3E3000)+3E54+3) H(H(H(999)-1)+H(17))
 kalo-ennecillion 1E(3E(3E3000)+3E57+3) H(H(H(999)-1)+H(18))
 kalo-icosillion 1E(3E(3E3000)+3E60+3) H(H(H(999)-1)+H(19))
 ... ... ...
 kalo-
enneennaconteennahectillion
 1E(3E(3E3000)+3E2997+3) H(H(H(999)-1)+H(998))
 kalo-killillion 1E(3E(3E3000)+3E3000+3) H(H(H(999)-1)+H(999))
 kalo-killo-untillion 1E(3E(3E3000)+3E3000+6) H(H(H(999)-1)+H(999)+1)
...
 ... ...
 kalo-killo-novemnonagintinongentillion 1E(3E(3E3000)+3E3000+3000) H(H(H(999)-1)+H(999)+999)
 kalo-killo-millillion 1E(3E(3E3000)+3E3000+3003) H(H(H(999)-1)+H(999)+1000)
 kalo-killo-milli-untillion 1E(3E(3E3000)+3E3000+3006) H(H(H(999)-1)+H(999)+1001)
 ... ... ...
 kalo-killo-micrillion 1E(3E(3E3000)+3E3000+
...
3E6+3)
 H(H(H(999)-1)+H(999)+H(1))
 kalo-killo-nanillion 1E(3E(3E3000)+3E3000+
...
3E9+3)
 H(H(H(999)-1)+H(999)+H(2))
 ... ... ...
 kalo-duokillillion 1E(3E(3E3000)+6E3000+3) H(H(H(999)-1)+2*H(999))
 kalo-trekillillion 1E(3E(3E3000)+9E3000+3) H(H(H(999)-1)+3*H(999))
 ... ... ...
 kalo-
novemnonagintinongentikillillion
 1E(3E(3E3000)+2.997E3003+3) H(H(H(999)-1)+999*H(999))
 kalo-killamillillion 1E(3E(3E3000)+3E3003+3) H(H(H(999)-1)+H(1000))
 ... ... ...
 kalo-killamicrillion 1E(3E(3E3000)+3E3006+3) H(H(H(999)-1)+H(1001))
 kalo-killananillion 1E(3E(3E3000)+3E3009+3) H(H(H(999)-1)+H(1002))
 ... ... ...
 kalo-
killaenneennaconteennahectillion
 1E(3E(3E3000)+3E5997+3)H(H(H(999)-1)+H(1998))
 kalo-
killaenneennaconteennahecto-
untillion
 1E(3E(3E3000)+3E5997+6) H(H(H(999)-1)+H(1998)+1)
 ... ... ...
 kalo-micrekillillion 1E(3E(3E3000)+3E6000+3) H(H(H(999)-1)+H(1999))
 kalo-micrekillo-untillion 1E(3E(3E3000)+3E6000+6)H(H(H(999)-1)+H(1999)+1)
 ... ... ...
 kalo-micrekillo-millillion 1E(3E(3E3000)+3E6000+3003) H(H(H(999)-1)+H(1999)+1000)
 ... ... ...
 kalo-micrekillamillillion 1E(3E(3E3000)+3E6003+3) H(H(H(999)-1)+H(2000))
 kalo-micrekillamicrillion 1E(3E(3E3000)+3E6006+3) H(H(H(999)-1)+H(2001))
 ... ... ...
 kalo-micrekilla
enneennaconteennahectillion
 1E(3E(3E3000)+3E8997+3) H(H(H(999)-1)+H(2998))
 kalo-nanekillillion 1E(3E(3E3000)+3E9000+3) H(H(H(999)-1)+H(2999))
 ... ... ...
 kalo-picekillillion 1E(3E(3E3000)+3E12,000+3) H(H(H(999)-1)+H(3999))
 kalo-femtekillillion 1E(3E(3E3000)+3E15,000+3) H(H(H(999)-1)+H(4999))
 kalo-attekillillion 1E(3E(3E3000)+3E18,000+3) H(H(H(999)-1)+H(5999))
 kalo-zeptekillillion 1E(3E(3E3000)+3E21,000+3) H(H(H(999)-1)+H(6999))
 kalo-yoctekillillion 1E(3E(3E3000)+3E24,000+3) H(H(H(999)-1)+H(7999))
 ... ... ...
 kalo-
enneennaconteennahectekilla
enneennaconteennahectillion
 1E(3E(3E3000)+3E(3E6-3)+3) H(H(H(999)-1)+H(999,998))
 kalo-megillion 1E(3E(3E3000)+3E(3E6)+3) H(H(H(999)-1)+H(999,999))
 kalo-mego-untillion 1E(3E(3E3000)+3E(3E6)+6) H(H(H(999)-1)+H(999,999)+1)
 ... ... ...
 kalo-mego-millillion
 1E(3E(3E3000)+3E(3E6)+3003)H(H(H(999)-1)+H(999,999)+1000)
 ... ... ...
 kalo-megamillillion 1E(3E(3E3000)+3E(3E6+3)+3) H(H(H(999)-1)+H(H(1)))
 ... ... ...
 kalo-
enneennaconteennahectemega-
enneennaconteennahectekilla-
enneennaconteennahectillion
 1E(3E(3E3000)+3E(3E9-3)+3) H(H(H(999)-1)+H(H(2)-2))
 kalo-gigillion 1E(3E(3E3000)+3E(3E9)+3) H(H(H(999)-1)+H(H(2)-1))
 kalo-gigo-untillion 1E(3E(3E3000)+3E(3E9)+6) H(H(H(999)-1)+H(H(2)-1)+1)
 ... ... ...
 kalo-terillion 1E(3E(3E3000)+3E(3E12)+3) H(H(H(999)-1)+H(H(3)-1))
 kalo-tero-untillion 1E(3E(3E3000)+3E(3E12)+6) H(H(H(999)-1)+H(H(3)-1)+1)
 ... ... ...
 kalo-petillion 1E(3E(3E3000)+3E(3E15)+3) H(H(H(999)-1)+H(H(4)-1))
 kalo-exillion 1E(3E(3E3000)+3E(3E18)+3) H(H(H(999)-1)+H(H(5)-1))
 kalo-zettillion 1E(3E(3E3000)+3E(3E21)+3) H(H(H(999)-1)+H(H(6)-1))
 kalo-yottillion 1E(3E(3E3000)+3E(3E24)+3) H(H(H(999)-1)+H(H(7)-1))
 ... ... ...
 kalo-nonecxenillion 1E(3E(3E3000)+3E(3E2997)+3) H(H(H(999)-1)+H(H(H(998)-1))
 kalo-nonecxeno-untillion 1E(3E(3E3000)+3E(3E2997)+6) H(H(H(999)-1)+H(H(H(998)-1)+1)
 ... ... ...
 duokalillion 1E(6E(3E3000)+3) H(2*H(H(999)-1))
 trekalillion 1E(9E(3E3000)+3) H(3*H(H(999)-1))
 quattuorkalillion 1E(12E(3E3000)+3) H(4*H(H(999)-1))
 ... ... ...
 novemnonagintinongentikalillion 1E(2.997E(3E3000+3)+3) H(999*H(H(999)-1))
 kalamillillion 1E(3E(3E3000+3)+3) H(H(H(999)))
 kalamilli-untillion 1E(3E(3E3000+3)+6) H(H(H(999))+1)
 ...
 ... ...
 kala-micrillion 1E(3E(3E3000+6)+3) H(H(H(999)+1))
 kala-nanillion 1E(3E(3E3000+9)+3) H(H(H(999)+2))
 ... ... ...
 kala-killillion 1E(3E(3E3000+3000)+3) H(H(H(999)+999))
 kala-megillion 1E(3E(3E3000+3E6)+3) H(H(H(999)+H(1)-1))
 kala-gigillion 1E(3E(3E3000+3E9)+3) H(H(H(999)+H(2)-1))
 kala-terillion 1E(3E(3E3000+3E12)+3) H(H(H(999)+H(3)-1))
 kala-petillion 1E(3E(3E3000+3E15)+3) H(H(H(999)+H(4)-1))
 ... ......
 kala-nonecxenillion 1E(3E(3E3000+3E2997)+3) H(H(H(999)+H(998)-1))
 micrekalillion 1E(3E(6E3000)+3) H(H(2*H(999)-1))
nanekalillion
 1E(3E(9E3000)+3) H(H(3*H(999)-1))
 ... ... ...
enneennaconteennahectekalillion
 1E(3E(2.997E3003)+3) H(H(H(999*H(999)-1))
 ... ... ...
 kalikillillion 1E(3E(3E3003)+3) H(H(H(1000)-1))
 kalimegillion 1E(3E(3E3006)+3) H(H(H(1001)-1))
 kaligigillion 1E(3E(3E3009)+3) H(H(H(1002)-1))
 kaliterillion 1E(3E(3E3012)+3) H(H(H(1003)-1))
 kalipetillion 1E(3E(3E3015)+3) H(H(H(1004)-1))
 ... ... ...
 kalinonecxenillion 1E(3E(3E5997)+3) H(H(H(1998)-1))
 dalillion 1E(3E(3E6000)+3) H(H(H(1999)-1))
 dalo-untillion 1E(3E(3E6000)+6) H(H(H(1999)-1)+1)
 ... ... ...
 duodalillion 1E(6E(3E6000)+3) H(2*H(H(1999)-1))
 ... ... ...
 dalamillillion 1E(3E(3E6000+3)+3) H(H(H(1999)))
 ... ... ...
 micredalillion 1E(3E(6E6000)+3) H(H(2*H(1999)-1))
 ... ... ...
 dalikillillion 1E(3E(3E6003)+3) H(H(H(2000)-1))
 dalimegillion 1E(3E(3E6006)+3) H(H(H(2001)-1))
 ... ... ...
 dalinonecxenillion 1E(3E(3E8997)+3) H(H(H(2998)-1))
 tralillion 1E(3E(3E9000)+3) H(H(H(2999)-1))
 tralo-untillion 1E(3E(3E9000)+6) H(H(H(2999)-1)+1)
 ... ... ...
 duotralillion 1E(6E(3E9000)+3) H(2*H(H(2999)-1))
 ... ... ...
 tralamillillion 1E(3E(3E9000+3)+3) H(H(H(2999)))
 ... ... ...
 micretralillion 1E(3E(6E9000)+3) H(H(2*H(2999)-1))
 ... ... ...
 tralikillillion 1E(3E(3E9003)+3) H(H(H(3000)-1))
 tralimegillion1E(3E(3E9006)+3)
 H(H(H(3001)-1))
 ... ... ...
 tralinonecxenillion 1E(3E(3E11,997)+3) H(H(H(3998)-1))
 talillion 1E(3E(3E12,000)+3) H(H(H(3999)-1))
 talo-untillion 1E(3E(3E12,000)+6) H(H(H(3999)-1)+1)
 ... ... ...
 talamillillion 1E(3E(3E12,000+3)+3) H(H(H(3999)))
 ... ... ...
 talikillillion 1E(3E(3E12,003)+3) H(H(H(4000)-1))
...
 ... ...
 palillion 1E(3E(3E15,000)+3) H(H(H(4999)-1))
 palo-untillion 1E(3E(3E15,000)+6) H(H(H(4999)-1)+1)
 ... ... ...
 palamillillion 1E(3E(3E15,000+3)+3) H(H(H(4999)))
 ... ... ...
 palikillillion 1E(3E(3E15,003)+3) H(H(H(5000)-1))
 ... ... ...
 exalillion 1E(3E(3E18,000)+3) H(H(H(5999)-1))
 exalo-untillion 1E(3E(3E18,000)+6) H(H(H(5999)-1)+1)
 ... ... ...
 exalamillillion 1E(3E(3E18,000+3)+3) H(H(H(5999)))
 ... ... ...
 exalikillillion 1E(3E(3E18,003)+3) H(H(H(6000)-1))
 ... ... ...
 zalillion 1E(3E(3E21,000)+3) H(H(H(6999)-1))
 zalo-untillion 1E(3E(3E21,000)+6) H(H(H(6999)-1)+1)
 ... ... ...
 zalamillillion 1E(3E(3E21,000+3)+3) H(H(H(6999)))
...
 ... ...
 zalikillillion 1E(3E(3E21,003)+3) H(H(H(7000)-1))
 ... ... ...
 yalillion 1E(3E(3E24,000)+3) H(H(H(7999)-1))
 yalo-untillion 1E(3E(3E24,000)+6) H(H(H(7999)-1)+1)
 ... ... ...
 yalamillillion 1E(3E(3E24,000+3)+3) H(H(H(7999)))
 ... ... ...
 yalikillillion 1E(3E(3E24,003)+3) H(H(H(8000)-1))
 ... ... ...
 nalillion 1E(3E(3E27,000)+3) H(H(H(8999)-1))
 nalo-untillion 1E(3E(3E27,000)+6) H(H(H(8999)-1)+1)
 ... ... ...
 nalamillillion 1E(3E(3E27,000+3)+3) H(H(H(8999)))
 ... ... ...
 nalikillillion 1E(3E(3E27,003)+3) H(H(H(9000)-1))
 ... ... ...
 dakalillion 1E(3E(3E30,000)+3) H(H(H(9999)-1))
 dakalo-untillion 1E(3E(3E30,000)+6)H(H(H(9999)-1)+1)
 ... ... ...
 dakalamillillion 1E(3E(3E30,000+3)+3) H(H(H(9999)))
 ... ... ...
 dakalikillillion1E(3E(3E30,003)+3)
H(H(H(10,000)-1))
 ... ... ...
hendakalillion
 1E(3E(3E33,000)+3)H(H(H(10,999)-1))
 hendakalo-untillion 1E(3E(3E33,000)+6) H(H(H(10,999)-1)+1)
 ... ... ...
 hendakalamillillion 1E(3E(3E33,000+3)+3) H(H(H(10,999)))
 ... ... ...
 hendakalikillillion 1E(3E(3E33,003)+3) H(H(H(11,000)-1))
 ... ... ...
 dokalillion 1E(3E(3E36,000)+3) H(H(H(11,999)-1))
 dokalo-untillion 1E(3E(3E36,000)+6) H(H(H(11,999)-1)+1)
 ... ... ...
 dokalamillillion 1E(3E(3E36,000+3)+3) H(H(H(11,999)))
 ... ... ...
 dokalikillillion 1E(3E(3E36,003)+3) H(H(H(12,000)-1))
 ... ... ...
 tradakalillion 1E(3E(3E39,000)+3) H(H(H(12,999)-1))
 tradakalo-untillion 1E(3E(3E39,000)+6) H(H(H(12,999)-1)+1)
 ... ... ...
 tradakalamillillion 1E(3E(3E39,000+3)+3) H(H(H(12,999)))
 ... ... ...
 tradakalikillillion 1E(3E(3E39,003)+3) H(H(H(13,000)-1))
 ... ... ...
 tedakalillion 1E(3E(3E42,000)+3) H(H(H(13,999)-1))
 tedakalo-untillion 1E(3E(3E42,000)+6) H(H(H(13,999)-1)+1)
 ... ... ...
 tedakalamillillion 1E(3E(3E42,000+3)+3) H(H(H(13,999)))
 ... ... ...
 tedakalikillillion 1E(3E(3E42,003)+3) H(H(H(14,000)-1))
 ... ... ...
 pedakalillion 1E(3E(3E45,000)+3) H(H(H(14,999)-1))
 pedakalo-untillion 1E(3E(3E45,000)+6) H(H(H(14,999)-1)+1)
 ... ... ...
 pedakalamillillion 1E(3E(3E45,000+3)+3) H(H(H(14,999)))
 ... ... ...
 pedakalikillillion 1E(3E(3E45,003)+3) H(H(H(15,000)-1))
 ... ... ...
 exadakalillion 1E(3E(3E48,000)+3) H(H(H(15,999)-1))
 exadakalo-untillion 1E(3E(3E48,000)+6) H(H(H(15,999)-1)+1)
 ... ... ...
 exadakalamillillion 1E(3E(3E48,000+3)+3) H(H(H(15,999)))
 ... ... ...
 exadakalikillillion 1E(3E(3E48,003)+3) H(H(H(16,000)-1))
 ... ... ...
 zedakalillion 1E(3E(3E51,000)+3) H(H(H(16,999)-1))
 zedakalo-untillion 1E(3E(3E51,000)+6) H(H(H(16,999)-1)+1)
 ... ... ...
 zedakalamillillion 1E(3E(3E51,000+3)+3) H(H(H(16,999)))
 ... ... ...
 zedakalikillillion 1E(3E(3E51,003)+3) H(H(H(17,000)-1))
 ... ... ...
 yodakalillion 1E(3E(3E54,000)+3)
 H(H(H(17,999)-1))
 nedakalillion 1E(3E(3E57,000)+3) H(H(H(18,999)-1))
 ikalillion 1E(3E(3E60,000)+3) H(H(H(19,999)-1))
 hotalillion 1E(3E(3E300,000)+3) H(H(H(99,999)-1))
 mejillion 1E(3E(3E3,000,000)+3) H(H(H(999,999)-1))
 dakejillion 1E(3E(3E30,000,000)+3) H(H(H(9,999,999)-1))
 hotejillion 1E(3E(3E300,000,000)+3) H(H(H(99,999,999)-1))
 gijillion 1E(3E(3E(3E9))+3) H(H(H(H(2)-1)-1))
 dakijillion 1E(3E(3E(30E9))+3) H(H(H(10*H(2)-1)-1))
 hotijillion 1E(3E(3E(300E9))+3) H(H(H(100*H(2)-1)-1))
 astillion 1E(3E(3E(3E12))+3) H(H(H(H(3)-1)-1))
 dakastillion 1E(3E(3E(30E12))+3) H(H(H(10*H(3)-1)-1))
 hotastillion 1E(3E(3E(300E12))+3) H(H(H(100*H(3)-1)-1))
 lunillion 1E(3E(3E(3E15))+3) H(H(H(H(4)-1)-1))
 dakunillion 1E(3E(3E(30E15))+3) H(H(H(10*H(4)-1)-1))
 hotunillion 1E(3E(3E(300E15))+3) H(H(H(100*H(4)-1)-1))
 fermillion 1E(3E(3E(3E18))+3) H(H(H(H(5)-1)-1))
 dakermillion 1E(3E(3E(30E18))+3) H(H(H(10*H(5)-1)-1))
 hotermillion 1E(3E(3E(300E18))+3) H(H(H(100*H(5)-1)-1))
 jovillion 1E(3E(3E(3E21))+3) H(H(H(H(6)-1)-1))
 dakovillion 1E(3E(3E(30E21))+3) H(H(H(10*H(6)-1)-1))
 hotovillion 1E(3E(3E(300E21))+3) H(H(H(100*H(6)-1)-1))
 solillion 1E(3E(3E(3E24))+3) H(H(H(H(7)-1)-1))
 dakolillion 1E(3E(3E(30E24))+3) H(H(H(10*H(7)-1)-1))
 hotolillion 1E(3E(3E(300E24))+3) H(H(H(100*H(7)-1)-1))
 betillion 1E(3E(3E(3E27))+3) H(H(H(H(8)-1)-1))
 daketillion 1E(3E(3E(30E27))+3) H(H(H(10*H(8)-1)-1))
 hotetillion 1E(3E(3E(300E27))+3) H(H(H(100*H(8)-1)-1))
glocillion
 1E(3E(3E(3E30))+3) H(H(H(H(9)-1)-1))
 dakocillion 1E(3E(3E(30E30))+3) H(H(H(10*H(9)-1)-1))
 hotocillion 1E(3E(3E(300E30))+3) H(H(H(100*H(9)-1)-1))
 gaxillion 1E(3E(3E(3E33))+3) H(H(H(H(10)-1)-1))
 dakaxillion 1E(3E(3E(30E33))+3) H(H(H(10*H(10)-1)-1))
 hotaxillion 1E(3E(3E(300E33))+3) H(H(H(100*H(10)-1)-1))
 supillion 1E(3E(3E(3E36))+3) H(H(H(H(11)-1)-1))
 dakupillion 1E(3E(3E(30E36))+3) H(H(H(10*H(11)-1)-1))
 hotupillion 1E(3E(3E(300E36))+3) H(H(H(100*H(11)-1)-1))
 versillion 1E(3E(3E(3E39))+3) H(H(H(H(12)-1)-1))
 dakersillion 1E(3E(3E(30E39))+3) H(H(H(10*H(12)-1)-1))
 hotersillion 1E(3E(3E(300E39))+3) H(H(H(100*H(12)-1)-1))
 multillion 1E(3E(3E(3E42))+3) H(H(H(H(13)-1)-1))
 dakultillion 1E(3E(3E(30E42))+3) H(H(H(10*H(13)-1)-1))
 hotultillion 1E(3E(3E(300E42))+3) H(H(H(100*H(13)-1)-1))
 nonecxenultillion 1E(3E(3E(2.997E45))+3)H(H(H(999*H(13)-1)-1))
 nonecxenulti-
nonecxenersi-
nonecxenupi-
nonecxenaxi-
nonecxenoci-
nonecxeneti-
nonecxenoli-
nonecxenovi-
nonecxenermi-
nonecxenuni-
nonecxenasti-
nonecxeniji-
nonecxeneji-
nonecxenali-
nonecxenillion
 1E(3E(3E(3E45-3))+3) H(H(H(H(14)-2)-1))

    We are now nearly at the end of our journey. Of coarse the last entry above is not the largest number we can name in Bowers' system; It merely represents the largest Class 3 Separator. If we form the largest Class 2 separator, and thereby the largest illion, we obtain the number 1E(3E(3E(3E45))). If we form the largest Class 1 Separator, and thereby the largest number, we obtain 1E(3E(3E(3E45))+3)-1.

    There are no larger numbers we can name in Bowers' system past 1E(3E(3E(3E45))+3)-1. To continue we would need a Class 4 Separator past the "multi". I mentioned this to bowers and suggested either using "omni" for omniverse to form "omnillion", or "cosmosillion" from "cosmos". Writing back he said that we preferred the use of "cosmillion". What then? We would need yet another Class 4 Separator to continue. We could have course fill out the Tier 4 Table, so that we could have the maximum of 999 Class 4 Separators. Yet the largest number expressible would still be finite, or put more poignantly, there would still be numbers without name! That's right Bowers' system can not name all numbers. Even if we continued to the 5th, 6th, 7th, 8th, 9th, 10th Tier, still there would be the nameless hordes beyond. Is counting, in the absolute sense, impossible then?! Will there always be numbers we can not name, and therefore can not count! That is, is it impossible to give unique names to all the counting numbers?! The surprising answer is, ... no, it is not impossible. We could for example name every number by reading out its digits. The problem is that even smallish large numbers would be difficult to say and understand. For example a 1,000,000 would be "one zero zero zero zero zero zero". One would have to count to write it, say it, read it, and hear it. Not an ideal form of communication by any means. Yet every number would have a name.

    The problem therefore is NOT giving every number a name, but rather giving it a name that is comprehensible. What is meant by "comprehensible"? Well one definition might be that the name is short enough to be able to say in a reasonably short amount of time, say 10 seconds or less. The problem is that there are only a finite number of combination's of sounds that can fit within 10 seconds. Inevitably, no matter how we choose to name ALL numbers, there will only be a finite number of them that can fit within some reasonable temporal or spatial interval, and an infinite number that can not. The solution that english is pointedly trying to achieve is not to give every number a short name, but to provide certain milestone numbers with short names. Bowers' system is simply an evolved and advanced form of the same impulse. English allows us to give a tremendous number like 1E63 a relatively short name such as "vigintillion". The catch is that names within its vicinity will be very long. Note however, that after awhile even the use of illions becomes long for certain names such as novemnonagintinongentimicro-novemnonagintinongenti-milli-novemnonagintinongentillion. When this happens there is yet a second level of name shortening, then a third, a fourth, and so on. Yet in these types of systems we don't have the same open endedness as other approaches. Is it possible to devise a system which names every number, and for every "short name" there is always, eventually some very very large number later on that must have an equally short name. This too must be impossible, because there are only a finite number of such short names. The best we can do is delay the inevitable. However at some point, in any open ended naming scheme, there must be an infinite horde of unpronounable seemingly endless named numbers, without a single short name among them!

    Does that seem mind boggling? Well here is an even more mind boggling truth, ... we can describe some of these numbers, but we can't do it with language alone. As long as we attempt to "name" EVERY number we are actually holding ourselves back. Once we move beyond into the nameless horde there is only one proper way to continue ... mathematics. This is the ticket required on the train ride to the infinite. Even in our attempts to avoid anything technical on our way to the very very large, mathematical logic was sneaking in. The way that the names are constructed is very regular and when seen properly is really a recursive process. It is recursion that will let us continue beyond the named and into the nameless. In fact we can already think about these numbers if we let go of our attempts to provide roots and names. Imagine a number that would require a 100 Tier root table, a 1000 Tier root table, a million, a billion, ... I'll let you imagine where that thinking leads :)

    That very thought is recursive in nature. Note that there is nothing so difficult or strange about it. Anyone is capable of recursive thinking. You don't need to be a mathematical wizard to understand it, I believe it is an innate form of thinking.

    We have reached the limits of our amateur excursion into the very large. To progress further we will need to explore the mathematical implications of what we have begun. What we have learned about exponents, scientific notation, and extending the illion series has a definite mathematical consequence. The results of this will lead to a very surprising revelation: numbers much larger than you might ever have imagined possible!

    In the next chapter we will explore recursion for the first time, and begin generating numbers so large that everything in the first two sections will pale in comparison.

    If your prepared to take this game to the next level, check out chapter 3-1.

    More content for Chapter 2-4 and 3-1 coming soon: Winter 2011 ! Stay tuned ...

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