Extended Tier 4 -illions and beyond

Part 1

Update 3rd September, 2022: I scrapped this system based on this version. Please check the new -illions right!

Introduction

Extensions

Illion function

Bowers' Tier 4 -illions fix

Extended Tier 4 -illions

I am going to make a large naming system reformation by me, inspired by CompactStar and Aarex Tiaokhiao.

Links:

https://integralview.wordpress.com/2020/10/01/extended-tier-4-to-6-illions/ - CompactStar's extended Tier 4 to Tier 6 -illions, proposed on 1st October, 2020 - For Extended Tier 4 -illions

My extended Tier 4 to Tier 6 -illions - The Grand Science v2

https://docs.google.com/document/d/1dhCjmN9_qOyydKY6a_rzbCfNg8yIGslEPVfA9iz60Ig/edit - Aarex Tiaokhiao's extended intermediate -illions, continued

Introduction

From early history, humans thought of an extensible naming system for grouping large numbers. That is, in English, we group with millions, billions, and trillions. Around the 20th century, mathematicians proposed new illions that haven't been seen from the real world before.

In the early 2000s, Jonathan Bowers decided to start his extensive list of illions, including numbers that reach beyond the realistic range. Sbiis, on the other hand, released the extensible system for Bowers' -illions, with all naming gaps filled out. (Sbiis Saibian's version)

Out of curiosity, Douglas Shamlin Jr. pointed out there was a small mistake that the petillion is ambiguous from his list. He fixed the problem by putting another e for tier 3 multipliers to -et root. He also published the LNGI page for Saibian' illions which is shown below. (Numbers Getting Bigger - illions version)

With problems fixed, we could name numbers up to the limit of Bowers' illions, which is the supremum of all tier 0 - 4 roots being used.

In this page, I am going to take Sbiis' and Douglas' spirits and continue the journey of never-ending illions list. Get ready, let’s reach out of the ethereal illions!

Extensions

Rise out of Bowers' illions, there are joints to different possibilities! One is spreading out to a tetrational range which metaness can't keep up!

In early 2020s, Nirvana (now CompactStar) decided to extend, up to the ridiculous limit of the Tier 6 system!

Regardless of only milestones, some existing names are gathered for amalgamates…

CompactStar's -illions

Not only that, there’s many systems of -illions going after multillion like:

15th Tier 4: metillion (me & CompactStar) / pyrillion / metalillion
1st Tier 5: redillion (me) / hepillion (CompactStar) / febrillion / keltillion / wektillion
1st Tier 6: hydrillion (me) / hapaxillion (CompactStar)
1st Tier 7: americillion (me) / redillion (by Aarex)
1st Tier 8: polonillion (me) / erkillion
1st Tier 9: israelillion (me) / izzillion
1st Tier 10: indillion (me) / meakoowillion

And so infinitum. (Note that I am not going to make intermediate values for Tamara’s illions)

Note that I am going to make two systems instead of one in one project, with the first system has no specific system name, and the another one is also called as "Modified CompactStar's system".

Illion function

Unfortunately, the Extensible Illion System is ill-defined. Aarex Tiaokhiao decided to define a new function by himself:

Ha = Ha#1
Ha#0 = 1,000*a
b > 0: Ha#b = H(1,000^a)#(b-1)

Examples:

H34 = H34#1 = H(1,000^34)#0 = 1,000*1,000^34 = 10^105 = 1 quattourtrigintillion
H2,013#2 = H(1,000^2,013)#1 = 1,000^(1,000^2,013+1) = 10^(3*10^6,039+3) = 1 micrekillatrecillion

Illion Function can also be expressed in Hyper-E notation: Ha#b = 1,000*E[1,000]a#b (base 1,000 Hyper-E notation)

And can be estimated approximately: 1,000^^(b+1) > Ha#b > 1,000^^b (for a < 333)

Bowers' Tier 4 -illions fix

Miserly, the "yoc" root based on Saibian's generalization on Tier 3 multiplicative to Tier 4 (from y + gloc) collides with some of the pre-defined Tier 3 -illions as follows:

10^(3*10^(3*10^(2.4*10^31+3))+3) => yocenillion
10^(3*10^(3*10^(2.4*10^31+6))+3) => yocodillion (collision detected!)
10^(3*10^(3*10^(2.4*10^31+9))+3) => yoctrillion (collision detected!)
10^(3*10^(3*10^(2.4*10^31+12))+3) => yocterillion (collision detected!)
10^(3*10^(3*10^(2.4*10^31+15))+3) => yocpetillion (collision detected!)
10^(3*10^(3*10^(2.4*10^31+18))+3) => yocectillion
10^(3*10^(3*10^(2.4*10^31+21))+3) => yoczetillion (collision detected!)
10^(3*10^(3*10^(2.4*10^31+24))+3) => yocyotillion
10^(3*10^(3*10^(2.4*10^31+27))+3) => yocxenillion (collision detected!)

So I will fix some connection ambiguity for the Tier 3 additive to Tier 4 root "yoc" when it follows -od, -tr, -ter, -pet, -zet, and -xen, by adding "i" after yoc, so we have:

10^(3*10^(3*10^(2.4*10^31+3))+3) => yocenillion
10^(3*10^(3*10^(2.4*10^31+6))+3) => yociodillion (resolved)
10^(3*10^(3*10^(2.4*10^31+9))+3) => yocitrillion (resolved)
10^(3*10^(3*10^(2.4*10^31+12))+3) => yociterillion (resolved)
10^(3*10^(3*10^(2.4*10^31+15))+3) => yocipetillion (resolved)
10^(3*10^(3*10^(2.4*10^31+18))+3) => yocectillion
10^(3*10^(3*10^(2.4*10^31+21))+3) => yocizetillion (resolved)
10^(3*10^(3*10^(2.4*10^31+24))+3) => yocyotillion
10^(3*10^(3*10^(2.4*10^31+27))+3) => yocixenillion (resolved)

But why these do not apply with higher "lone" Tier 3 roots for Tier 3 additives to yoc such as:

10^(3*10^(3*10^(2.4*10^31+30))+3) => yocdakillion
10^(3*10^(3*10^(2.4*10^31+33))+3) => yochendillion
10^(3*10^(3*10^(2.4*10^31+36))+3) => yocdokillion
10^(3*10^(3*10^(2.4*10^31+39))+3) => yoctradakillion
10^(3*10^(3*10^(2.4*10^31+42))+3) => yoctedakillion
10^(3*10^(3*10^(2.4*10^31+60))+3) => yocikillion
10^(3*10^(3*10^(2.4*10^31+90))+3) => yoctrakillion
10^(3*10^(3*10^(2.4*10^31+120))+3) => yoctekillion
10^(3*10^(3*10^(2.4*10^31+300))+3) => yochotillion
10^(3*10^(3*10^(2.4*10^31+600))+3) => yocbotillion
10^(3*10^(3*10^(2.4*10^31+900))+3) => yoctrotillion
10^(3*10^(3*10^(2.4*10^31+1200))+3) => yoctotillion

And so on.

In addition, note that I will add "i" for Tier 3 additives to Tier 4 roots too, to avoid some ambiguity!

For example: 1.2*10^18th Tier 3 -illion: fermibotunillion

Extended Tier 4 -illions

Aarex Tiaokhiao's name: Hypercelestial · DeepLineMadom's name: Hypercosmological

[[ Improved by me TWICE!!! Original improvement here. ]]

Pre-definitions

Metillion = 10^(3*10^(3*10^(3*10^45))+3) [#15] => Metaverse
Xevillion = 10^(3*10^(3*10^(3*10^48))+3) [#16] => Xenoverse
Hypillion = 10^(3*10^(3*10^(3*10^51))+3) [#17] => Hyperverse
Omnillion = 10^(3*10^(3*10^(3*10^54))+3) [#18] => Omniverse
Outillion = 10^(3*10^(3*10^(3*10^57))+3) [#19] => The Outside
Barrillion = 10^(3*10^(3*10^(3*10^60))+3) [#20] => The Barrel
Barralillion = 10^(3*10^(3*10^(3*10^63))+3) [#21] => Barr+kal
Barrejillion = 10^(3*10^(3*10^(3*10^66))+3) [#22] => Barr+mej
Barrijillion = 10^(3*10^(3*10^(3*10^69))+3) [#23] => Barr+gij
Barrastillion = 10^(3*10^(3*10^(3*10^72))+3) [#24] => Barr+ast
Barrunillion = 10^(3*10^(3*10^(3*10^75))+3) [#25] => Barr+lun
Barrermillion = 10^(3*10^(3*10^(3*10^78))+3) [#26] => Barr+ferm
Barrovillion = 10^(3*10^(3*10^(3*10^81))+3) [#27] => Barr+jov
Barresolillion = 10^(3*10^(3*10^(3*10^84))+3) [#28] => Barr+sol
Barretillion = 10^(3*10^(3*10^(3*10^87))+3) [#29] => Barr+bet
Garrillion = 10^(3*10^(3*10^(3*10^90))+3) [#30] => Gij*barr
Astarrillion = 10^(3*10^(3*10^(3*10^120))+3) [#40] => Ast*barr
Lunarrillion = 10^(3*10^(3*10^(3*10^150))+3) [#50] => Lun*barr
Fermarrillion = 10^(3*10^(3*10^(3*10^180))+3) [#60] => Ferm*barr
Jovarrillion = 10^(3*10^(3*10^(3*10^210))+3) [#70] => Jov*barr
Solarrillion = 10^(3*10^(3*10^(3*10^240))+3) [#80] => Sol*barr
Betarrillion = 10^(3*10^(3*10^(3*10^270))+3) [#90] => Bet*barr
Hutillion = 10^(3*10^(3*10^(3*10^300))+3) [#100] => Previous hundreds multipliers, similar to hot in Tier 3, predefined by Jonathan Bowers
Mutillion = 10^(3*10^(3*10^(3*10^600))+3) [#200] => Mej*hut
Gutillion = 10^(3*10^(3*10^(3*10^900))+3) [#300] => Gij*hut
Astutillion = 10^(3*10^(3*10^(3*10^1200))+3) [#400] => Ast*hut
Lutillion = 10^(3*10^(3*10^(3*10^1500))+3) [#500] => Lun*hut
Futillion = 10^(3*10^(3*10^(3*10^1800))+3) [#600] => Ferm*hut
Jutillion = 10^(3*10^(3*10^(3*10^2100))+3) [#700] => Jov*hut
Sutillion = 10^(3*10^(3*10^(3*10^2400))+3) [#800] => Sol*hut
Butillion = 10^(3*10^(3*10^(3*10^2700))+3) [#900] => Bet*hut

Generalization

Hang on… How I start at metillion? Guess what, the naming gaps were already filled. I was going meta for nonstandard illions whatsoever.
But, one ubiquitous issue. If I take met and put the first letter off, it would result the same as I do to bet. They are splitted into 2 identical "et."

(taking the first letter out: bet -> et, met -> et)

But did I stump on that? NO.

I want to do a similar resolution as what Douglas resolved. He decided to turn et and eet when the first letter (b) is removed.
This is consistent as you are adding Tier 3 multiplicatives to Tier 4.

(1st: Taking the first letter out: bet -> et,
2nd: Douglas' resolution, adding another e: et -> eet,
3rd: Finally, add Tier 3 roots as multiplicative: hot + eet -> hoteet)

This doesn't work for other tier multiplicatives and all additives:

(Tier 1 multiplicative: vigint + (i) + bet -> vigintibet)
(Tier 2 multiplicative: duec + (e) + bet -> duecebet)
(Tier 1 additive: bet + (o) + zept -> betozept)
(Tier 2 additive: bet + (a) + xenn -> betaxenn)
(Tier 3 additive: bet + (i) + mej -> betimej)

I eradicate met into ett for Tier 3 multiplicatives to met. In that case, take out the first letter and add another t after e.

(d + met - (m) + (t) -> dettillion)
(tr + met - (m) + (t) -> trettillion)
(t + met - (m) + (t) -> tettillion)
(dak + met - (m) + (t) -> dakettillion)

(sequence: metillion, dettillion, trettillion, tettillion, ..., nonecxenettillion)

Miserly, one collides with the existing zettillion…

(z + met - (m) + (t) -> zettillion: collision detected)

So the resolved variant for zettillion has to be degenerated to zeettillion. Just add another e, like Douglas!

(z + (e) + met - (m) + (t) -> zeettillion)

Now I can go hypercelestial and reach far out of natural cosmology! Let's blast at speeds of abstraction!

Welcome to the next level… The list of illions go wild out! o_0`

Now eradicate the first letters and mutate it on higher roots! This goes legionically worse;

1 => kal (multiplied root -al)
2 => mej (multiplied root -ej)
3 => gij (multiplied root -ij)
4 => ast (multiplied root -ast)
5 => lun (multiplied root -un)
6 => ferm (multiplied root -erm)
7 => jov (multiplied root -ov)
8 => sol (multiplied root -ol)
9 => bet (multiplied root -eet)
10 => gloc (multiplied root -oc)
11 => gax (multiplied root -ax)
12 => sup (multiplied root -up)
13 => vers (multiplied root -ers)
14 => mult (multiplied root -ult)
15 => met (multiplied root -ett) - [1] Exception: 7*10^45-th Tier 3 => zeettillion
16 => xev (multiplied root -ev)
17 => hyp (multiplied root -(oh)yp) - [2] (oh) is optional.
18 => omn(iv) (multiplied root -omn) - [3] With omnillion/omnivillion consensus, having an (iv) is also optional too.
19 => out (multiplied root -out) - [4] Formerly -ut before my improvement/reformation, since "o" is a vowel, hence the fix.

[1] Exception: 7*10^45-th Tier 3 => zeettillion

[2] (oh) is optional.

[3] With omnillion/omnivillion consensus, having an (iv) is also optional too.

[4] Formerly -ut before my improvement/reformation, since "o" is a vowel, hence the fix.

Onto the local scale of barrels and plexials; Repeat the process for placing a Tier 3 multiplicative by removing the first letter.

But when followed by "garr" and any hundred root not "hut" and "astut", add "o" in between instead for pronunciation.

So we have:

20 => barr (multiplied root -arr)
30 => garr (multiplied root -ogarr)
40 => astarr (multiplied root -astrr)
50 => lunarr (multiplied root -unarr)
60 => fermarr (multiplied root -ermrr)
70 => jovarr (multiplied root -ovarr)
80 => solarr (multiplied root -olarr)
90 => betarr (multiplied root -etarr)
100 => hut (multiplied root -ut)
200 => mut (multiplied root -omut)
300 => gut (multiplied root -ogut)
400 => astut (multiplied root -astut)
500 => lut (multiplied root -olut)
600 => fut (multiplied root -ofut)
700 => jut (multiplied root -ojut)
800 => sut (multiplied root -osut)
900 => but (multiplied root -obut)

Besides with Tier 3 multiplicatives to Tier 4… Let's fold the Tier 4 roots by generalizations of barr- series.

It has been recently tweaked to use most of tier 4 factors instead.

__1: -al
__2: -ej
__3: -ij
__4: -ast
__5: -un
__6: -erm
__7: -ov
__8: -esol
__9: -et
_2_: barr-
_3_: garr-
_4_: astarr-
_5_: lunarr-
_6_: fermarr-
_7_: jovarr-
_8_: solarr-
_9_: betarr-

This allows us to name illions up to exactly hutillion, at 100th Tier 4!

Let's take a major step up from fictional cosmology, and observe the farthests.

"Hut Em' Down, Jut no Buts!"
~ Proto-Alien from Type 9.7 Archverse

"Lut the Hundreds up, delete the (t)s, and Gut the Ones and Tens on the right! That's we build the Huts of Hypercelestial Scales!"
"And let the Celestial Entity fix the “t” conflict after hundreds!"

This is extraordinary… If you didn't understand Tier 4, check the root table below:

Note: You can choose any option for (t/k)al, (t/m)ej, and (t/g)ij for one roots placed after hundreds. In particular, t is recommended.

Comparison with the old version:

New version

Originally by Aarex Tiaokhiao, improved by me

Old version

By Aarex Tiaokhiao

After that, the limit of the Bowers' polytope up to the limit of Tier 4 -illion is:

poly

nonecxenobubetarreti
nonecxenobubetarresoli
nonecxenobubetarrovi
nonecxenobubetarrermi
nonecxenobubetarruni
nonecxenobubetarrasti
nonecxenobubetarriji
nonecxenobubetarreji
nonecxenobubetarrali
nonecxenobubetarri
...
nonecxenarri-nonecxenouti-nonecxenomni-
nonecxenypi-nonecxenevi-nonecxenetti-
nonecxenulti-nonecxenersi-nonecxenupi-
nonecxenaxi-nonecxenoci-nonecxeneeti-
nonecxenoli-nonecxenovi-nonecxenermi-
nonecxenuni-nonecxenasti-nonecxeniji-
nonecxeneji-nonecxenalnonecxenon

And finally, Now we organize the huts of hundreds, here’s the list of all extended Tier-4 -illions!

Metillion = 10^(3*10^(3*10^(3*10^45))+3) [#15]
Dettillion = 10^(3*10^(3*10^(6*10^45))+3) [#15*2]
Trettillion = 10^(3*10^(3*10^(9*10^45))+3) [#15*3]
Tettillion = 10^(3*10^(3*10^(1.2*10^46))+3) [#15*4]
Zeettillion = 10^(3*10^(3*10^(2.1*10^46))+3) [#15*7]
Dakettillion = 10^(3*10^(3*10^(3*10^46))+3) [#15*10]
Hotettillion = 10^(3*10^(3*10^(3*10^47))+3) [#15*100]
Xevillion = 10^(3*10^(3*10^(3*10^48))+3) [#16]
Dakevillion = 10^(3*10^(3*10^(3*10^49))+3) [#16*10]
Hotevillion = 10^(3*10^(3*10^(3*10^50))+3) [#16*100]
Hypillion = 10^(3*10^(3*10^(3*10^51))+3) [#17]
Dakypillion = 10^(3*10^(3*10^(3*10^52))+3) [#17*10]
Hotypillion = 10^(3*10^(3*10^(3*10^53))+3) [#17*100]
Omnillion = 10^(3*10^(3*10^(3*10^54))+3) [#18]
Dakomnillion = 10^(3*10^(3*10^(3*10^55))+3) [#18*10]
Hotomnillion = 10^(3*10^(3*10^(3*10^56))+3) [#18*100]
Outillion = 10^(3*10^(3*10^(3*10^57))+3) [#19]
Dakoutillion = 10^(3*10^(3*10^(3*10^58))+3) [#19*10]
Hotoutillion = 10^(3*10^(3*10^(3*10^59))+3) [#19*100]
Barrillion = 10^(3*10^(3*10^(3*10^60))+3) [#20]
Dakarrillion = 10^(3*10^(3*10^(3*10^61))+3) [#20*10]
Hotarrillion = 10^(3*10^(3*10^(3*10^62))+3) [#20*100]
Barralillion = 10^(3*10^(3*10^(3*10^63))+3) [#21]
Barrejillion = 10^(3*10^(3*10^(3*10^66))+3) [#22]
Barrijillion = 10^(3*10^(3*10^(3*10^69))+3) [#23]
Barrastillion = 10^(3*10^(3*10^(3*10^72))+3) [#24]
Barrunillion = 10^(3*10^(3*10^(3*10^75))+3) [#25]
Barrermillion = 10^(3*10^(3*10^(3*10^78))+3) [#26]
Barrovillion = 10^(3*10^(3*10^(3*10^81))+3) [#27]
Barresolillion = 10^(3*10^(3*10^(3*10^84))+3) [#28]
Barretillion = 10^(3*10^(3*10^(3*10^87))+3) [#29]
Garrillion = 10^(3*10^(3*10^(3*10^90))+3) [#30]
Dakoarrillion = 10^(3*10^(3*10^(3*10^91))+3) [#30*10]
Hotogarrillion = 10^(3*10^(3*10^(3*10^92))+3) [#30*100]
Garralillion = 10^(3*10^(3*10^(3*10^93))+3) [#31]
Garrejillion = 10^(3*10^(3*10^(3*10^96))+3) [#32]
Garrijillion = 10^(3*10^(3*10^(3*10^99))+3) [#33]
Garrastillion = 10^(3*10^(3*10^(3*10^102))+3) [#34]
Garrunillion = 10^(3*10^(3*10^(3*10^105))+3) [#35]
Garrermillion = 10^(3*10^(3*10^(3*10^108))+3) [#36]
Garrovillion = 10^(3*10^(3*10^(3*10^111))+3) [#37]
Garresolillion = 10^(3*10^(3*10^(3*10^114))+3) [#38]
Garretillion = 10^(3*10^(3*10^(3*10^117))+3) [#39]
Astarrillion = 10^(3*10^(3*10^(3*10^120))+3) [#40]
Dakastarrillion = 10^(3*10^(3*10^(3*10^121))+3) [#40*10]
Astarralillion = 10^(3*10^(3*10^(3*10^123))+3) [#41]
Lunarrillion = 10^(3*10^(3*10^(3*10^150))+3) [#50]
Dakunarrillion = 10^(3*10^(3*10^(3*10^151))+3) [#50*10]
Lunarralillion = 10^(3*10^(3*10^(3*10^153))+3) [#51]
Fermarrillion = 10^(3*10^(3*10^(3*10^180))+3) [#60]
Dakermarrillion = 10^(3*10^(3*10^(3*10^181))+3) [#60*10]
Fermarralillion = 10^(3*10^(3*10^(3*10^183))+3) [#61]
Jovarrillion = 10^(3*10^(3*10^(3*10^210))+3) [#70]
Solarrillion = 10^(3*10^(3*10^(3*10^240))+3) [#80]
Betarrillion = 10^(3*10^(3*10^(3*10^270))+3) [#90]
Betarretillion = 10^(3*10^(3*10^(3*10^297))+3) [#99]
Hutillion = 10^(3*10^(3*10^(3*10^300))+3) [#100]
Dakutillion = 10^(3*10^(3*10^(3*10^301))+3) [#100*10]
Hotutillion = 10^(3*10^(3*10^(3*10^302))+3) [#100*100]
Hutalillion = 10^(3*10^(3*10^(3*10^303))+3) [#101]
Hutejillion = 10^(3*10^(3*10^(3*10^306))+3) [#102]
Hutijillion = 10^(3*10^(3*10^(3*10^309))+3) [#103]
Hutastillion = 10^(3*10^(3*10^(3*10^312))+3) [#104]
Hulunillion = 10^(3*10^(3*10^(3*10^315))+3) [#105]
Hufermillion = 10^(3*10^(3*10^(3*10^318))+3) [#106]
Hujovillion = 10^(3*10^(3*10^(3*10^321))+3) [#107]
Husolillion = 10^(3*10^(3*10^(3*10^324))+3) [#108]
Hubetillion = 10^(3*10^(3*10^(3*10^327))+3) [#109]
Huglocillion = 10^(3*10^(3*10^(3*10^330))+3) [#110]
Hugaxillion = 10^(3*10^(3*10^(3*10^333))+3) [#111]
Husupillion = 10^(3*10^(3*10^(3*10^336))+3) [#112]
Huversillion = 10^(3*10^(3*10^(3*10^339))+3) [#113]
Humultillion = 10^(3*10^(3*10^(3*10^342))+3) [#114]
Humetillion = 10^(3*10^(3*10^(3*10^345))+3) [#115]
Huxevillion = 10^(3*10^(3*10^(3*10^348))+3) [#116]
Hutypillion = 10^(3*10^(3*10^(3*10^351))+3) [#117]
Hutomnillion = 10^(3*10^(3*10^(3*10^354))+3) [#118]
Hutoutillion = 10^(3*10^(3*10^(3*10^357))+3) [#119]
Hubarrillion = 10^(3*10^(3*10^(3*10^360))+3) [#120]
Hubarralillion = 10^(3*10^(3*10^(3*10^363))+3) [#121]
Hubarrejillion = 10^(3*10^(3*10^(3*10^366))+3) [#122]
Hubarrijillion = 10^(3*10^(3*10^(3*10^369))+3) [#123]
Hubarrastillion = 10^(3*10^(3*10^(3*10^372))+3) [#124]
Hubarrunillion = 10^(3*10^(3*10^(3*10^375))+3) [#125]
Hubarrermillion = 10^(3*10^(3*10^(3*10^378))+3) [#126]
Hubarrovillion = 10^(3*10^(3*10^(3*10^381))+3) [#127]
Hubarresolillion = 10^(3*10^(3*10^(3*10^384))+3) [#128]
Hubarretillion = 10^(3*10^(3*10^(3*10^387))+3) [#129]
Hugarrillion = 10^(3*10^(3*10^(3*10^390))+3) [#130]
Hutastarrillion = 10^(3*10^(3*10^(3*10^420))+3) [#140]
Hulunarrillion = 10^(3*10^(3*10^(3*10^450))+3) [#150]
Hufermarrillion = 10^(3*10^(3*10^(3*10^480))+3) [#160]
Hujovarrillion = 10^(3*10^(3*10^(3*10^510))+3) [#170]
Husolarrillion = 10^(3*10^(3*10^(3*10^540))+3) [#180]
Hubetarrillion = 10^(3*10^(3*10^(3*10^570))+3) [#190]
Mutillion = 10^(3*10^(3*10^(3*10^600))+3) [#200]
Dakomutillion = 10^(3*10^(3*10^(3*10^600))+3) [#200*10]
Hotomutillion = 10^(3*10^(3*10^(3*10^600))+3) [#200*100]
Mutalillion = 10^(3*10^(3*10^(3*10^603))+3) [#201]
Mutejillion = 10^(3*10^(3*10^(3*10^606))+3) [#202]
Muglocillion = 10^(3*10^(3*10^(3*10^630))+3) [#210]
Mugaxillion = 10^(3*10^(3*10^(3*10^633))+3) [#211]
Mubarrillion = 10^(3*10^(3*10^(3*10^660))+3) [#220]
Gutillion = 10^(3*10^(3*10^(3*10^900))+3) [#300]
Astutillion = 10^(3*10^(3*10^(3*10^1200))+3) [#400]
Lutillion = 10^(3*10^(3*10^(3*10^1500))+3) [#500]
Futillion = 10^(3*10^(3*10^(3*10^1800))+3) [#600]
Jutillion = 10^(3*10^(3*10^(3*10^2100))+3) [#700]
Sutillion = 10^(3*10^(3*10^(3*10^2400))+3) [#800]
Butillion = 10^(3*10^(3*10^(3*10^2700))+3) [#900]
Bubetarrillion = 10^(3*10^(3*10^(3*10^2970))+3) [#990]
Bubetarretillion = 10^(3*10^(3*10^(3*10^2997))+3) [#999]

And hence the Tier 3 limit of the Tier 4 generalized -illion is:

(alternatively:
nonecxenobubetarreti
nonecxenobubetarresoli
nonecxenobubetarrovi
nonecxenobubetarrermi
nonecxenobubetarruni
nonecxenobubetarrasti
nonecxenobubetarriji
nonecxenobubetarreji
nonecxenobubetarrali
nonecxenobubetarri
...
nonecxenarri-nonecxenouti-nonecxenomnivi-
nonecxenohypi-nonecxenevi-nonecxenetti-
nonecxenulti-nonecxenersi-nonecxenupi-
nonecxenaxi-nonecxenoci-nonecxeneeti-
nonecxenoli-nonecxenovi-nonecxenermi-
nonecxenuni-nonecxenasti-nonecxeniji-
nonecxeneji-nonecxenalnonecxenillion)

= (10^3,000-1)th Tier 3 -illion

= 10^(3*10^(3*10^(3*10^3,000-3))+3)

Before we get extraordinary, let's peek into the two proposals for Tier 5 -illions: CompactStar's system and my system!

Moving on other possibilities...

There's so many possibilities from obscure websites. They are even organized in a sheet. It is always fun, so why not explain in this page?

There is another name for 15th tier-4 -illion which is familiar to most googologists: pyrillion.

I think this is a combination of pyro and -illion, but let’s get over it.

Intermediate googologists just remove "p" for tier 3 multiplicatives. This is what I did:

"The second letter is y, and the first letter is p, so I use the alternative hypillion method. Just add an o- at the left of pyr- root!"

This coins dopyrillion, which is 2*10^45-th Tier-3 -illion, dakopyrillion, which is 10^46-th Tier-3 -illion, and several others.

But, is that it? Wrong. There are so many googologisms left to go. Here are the possibilities for Tier 4.

See other systems, or Czech out on https://docs.google.com/document/d/1dhCjmN9_qOyydKY6a_rzbCfNg8yIGslEPVfA9iz60Ig/edit!

Part 2 (Note: Parts beyond the first part are incomplete, so modifications can happen.)

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