Pointless Gigantic List of Numbers - Part 5 (E100#^#100 to E100#^^^#100)

Mossol

{10,10(1)10,100}

Evaluates to {10,10,10,10,10,10,10,10,10,10(1)9,100}.

Godthroogahlah

E100#^#*##100

Solves to E100#^#*#100#^#*#100#^#*#100.........#^#*#100 with 100 100’s. This is comparable to mossol.

Missol

{10,10(1)10,100,2}

Bossol

{10,10(1)10,10,100}

Godtetroogahlah

E100#^#*###100

Comparable to bossol.

Trossol

{10,10(1)10,10,10,100}

Godpentoogahlah

E100#^#*####100

Goddektoogahlah

E100#^#*#^#9

Diteral

{10,10(1)(1)2} = {10,10,10,10,10,10,10,10,10,10(1)10,10,10,10,10,10,10,10,10,10}

This evaluates to:

/10,10,10,10,10,10,10,10,10,10\

\10,10,10,10,10,10,10,10,10,10/.

Right around the limit of 2-row arrays. Now on to higher-level planar arrays!

The Planar-Array Range

{10,100(1)(1)2} - {a,b(2)2}

(order type w^(w2) ~ w^w^2)

Entries: 25

Dubol

{10,100(1)(1)2}

Or

/10,10,10,10.........10\

\10,10,10,10.........10/ with 100 10s in each row. Yikes! This number is the start of 3-row arrays. By the way, (2) means move to the next plane, and {a,b(2)c} = {a,b(1)(1)(1)(1)........(1)c-1} with b (1)s, or a b*b array of a’s with c-1 behind the first a.

Also, note how for the low and high bound of the number range I’m using variables. This is because strict limits don’t feel right and I want the limit to just be a number expressible in the way shown. It also makes sense to use order types in the fast-growing hierarchy, because it's a very common way to approximate googologically large numbers.

Deutero-godgahlah

E100#^#*#^#100

This number is comparable to dubol, and not too far from E100#^##100. Now we’re really starting to get somewhere with our godgahlah extensions.

Dutrol

{10,100(1)(1)3}

Deutero-gotrigahlah

E100#^#*#^#100#^#*#^#100

Comparable to dutrol.

Admiral

{10,10(1)(1)10}

This is comparable to deutero-godekahlah, another military-themed Bowerian googolism.

Dossol

{10,10(1)(1)100}

Deutero-godgoldgahlah

E100#^#*#^#*#100

If we want to go anywhere we’ll need new delimiters (#....# expressions) altogether, like we’re doing. This number is comparable to dossol.

Cyperal

{65,googolplex(1)1000,googol(1)7quadragintiquingentillion,42}

This is just another one of the deleted googolisms on Googology Wiki, deleted because no external sources were given. It's a strange number alright.

Dutritri

{3,3(2)2} = {3,3,3(1)3,3,3(1)3,3,3}

Or

/3,3,3\

|3,3,3|

\3,3,3/ in array form. This is a square of nine threes.

Dutridecal

{10,3(2)2}

Or

/10,10,10\

|10,10,10|

\10,10,10/, This is replacing every entry in the enormous dutritri with a 10, but really not too much of an improvement. We’ll need to go better, and faster.

Triubol

{10,100(1)(1)(1)2}

A 3x100 array of 10s, and a number I coined.

Trito-godgahlah

E100#^#*#^#*#^#100 = E100#^##3

At last we’re in the realm of #^##. Whew, that was a long way. But we’re still a long way to #^#^# and an even longer way to #^^#.

A deutero-godgahlah is about a 2-row array, trito- is 3 rows.....you can guess what a teterto-godgahlah would be.

Tetrubol

{10,100(1)(1)(1)(1)2}

Comparable to teterto-godgahlah.

Teterto-godgahlah

E100#^#*#^#*#^#*#^#100 = E100#^##4

Comparable to a 100-length 4-row array of 10s.

Pepto-godgahlah

E100#^##5

Exto-godgahlah

E100#^##6

Epto-godgahlah

E100#^##7

Ogdo-godgahlah

E100#^##8

Ento-godgahlah

E100#^##9

Xappol

{10,10(2)2} = 10^2 & 10

The xappol is the result of solving 10x10 array of 10's in Bowers' notation. Here is that array written out:

/10,10,10,10,10,10,10,10,10,10\

|10,10,10,10,10,10,10,10,10,10|

|10,10,10,10,10,10,10,10,10,10|

|10,10,10,10,10,10,10,10,10,10|

/ 10,10,10,10,10,10,10,10,10,10 \

\ 10,10,10,10,10,10,10,10,10,10 /

|10,10,10,10,10,10,10,10,10,10|

|10,10,10,10,10,10,10,10,10,10|

|10,10,10,10,10,10,10,10,10,10|

\10,10,10,10,10,10,10,10,10,10/

YIKES! This number is a good example of a big planar array. It would require an inconceivably large number of levels of decomposition just to get rid of the last row, and even more unfathomably long to completely solve!

The name xappol has been honored in the name XappolBot of the bot (programmed by Vel!) in Googology Wiki's IRC chat.

Dekato-godgahlah

E100#^##10

Isosto-godgahlah

E100#^##20

Goxxol

{10,100(2)2}

Or a 100x100 array of 10s. Saibian coined this number as a number comparable to the next number.

Gridgahlah/hecato-godgahlah

E100#^##100

This is the first real good extension to a godgahlah. It’s much further than any naive extension of Hyper-E could dream of going, and yet it just looks like a slight extension. Bigger and better numbers are coming our way, be prepared. This number is also in the same general domain of numbers as Bowers’ xappol, even though this is significantly bigger.

Xappolplex

{10,xappol(2)2}

The planar array for this number would be too big to fit in the observable universe, or even for x observable universes where x is the number of Planck volumes in the universe - these numbers transcend any such analogy anyway. This number is the next step in recursion from a xappol.

The Multidimensional-Array Range

{a,b(2)2} - {a,b(c)2}

(order type w^w^2 ~ w^w^w)

Entries: 43

Grand xappol

{10,10(2)3}

Remember the array used to define a xappol? Put a 2 behind the first 10 and you get this. When you solve it to a planar array it would be horrendously huge, and then you'll need to go through insane decompositions just to even turn it into a linear array! However, with numbers this large this is a pretty modest improvement, as it's only doubling the order type!

Gridtrigahlah

E100#^##100#^##100

Notice how we’re zooming a lot quicker than previously. This number is comparable to grand xappol as gridgahlah is to xappol.

Gridtergahlah

E100#^##*#4

E100#^##*#100

Saibian does not define this and goes straight to bigger numbers, This number could probably be called a gridgoldgahlah.

E100#^##*##100

Could probably be called gridthroogahlah.

E100#^##*#^#100

This might be called a gridgodgahlah, I don't know. Saibian doesn't give a name for this number.

Deutero-gridgahlah

E100#^##*#^##100

Just as a deutero-godgahlah is 2 rows, a deutero-gridgahlah is 2 planes.

Dimentri

{3,3(3)2} = 3^3&3

Or {3,3,3(1)3,3,3(1)3,3,3(2)3,3,3(1)3,3,3(1)3,3,3(2)3,3,3(1)3,3,3(1)3,3,3} in full. This is a 3x3x3 cube of 27 3s and it's an unspeakable sized number in its own right. But it pales in comparison to the next numbers.

Trito-gridgahlah

E100#^##*#^##*#^##100

About a 100x100x3 cube of 10s. Now let’s skip to a Bowersism:

Colossol

{10,10(3)2}=10^3&10

This colossal number is a 10x10x10 CUBE of 10’s! It's a horrendous sized number of order type w^w^3, and decomposing it leads to insane levels of recursion. It was formerly called colossal.

Dekato-gridgahlah

E100#^###10

The closest Saibianism to a colossol.

Coloxxol

{10,100(3)2}=100^3&10

Instead of just a 10x10x10 cube of 10’s, this is a 100x100x100 cube of a million 10s! Saibian coined this to have a number comparable to kubikahlah.

Kubikahlah

E100#^###100

About a 100x100x100 CUBE of 10s! We’re really getting to awesome stuff with these epicly huge numbers. This number is reasonably close to a colossol.

Deutero-kubikahlah

E100#^###*#^###100

About a 100x100x100x2 tesseract of 10s! This number is heading straight into 4 dimensional arrays. How about....

Terossol

{10,10(4)2}=10^4&10

A 10x10x10x10 tesseract of 10s! Tesseracts can be drawn by hand quite easily, but still quite mind-boggling to imagine. They aren’t too bad compared to higer dimensions. Anyway, solving this number would requitre solving 10 cubes, each bigger than the previous! Each cube would requite lots and lots of squares to solve, and lots more linear arrays just to decompose the squares! You’d end up with a vast linear array, and it’ll take a grueling number of steps to solve that into the final number!

Dekato-kubikahlah

E100#^####10

Comparable to terossol.

Teroxxol

{10,100(4)2}

Instead of just 10 cubes, solving this would take 100 enormous cubes! Just imagining this boggles your mind greatly. But it pales in comparison to the insanity of tetrational arrays (seen in a bit).

Quarticahlah

E100#^####100

We’re almost to the realm of #^#^# numbers. This mind-boggling number is about a 100^4 tesseract of 10s! Solving the Cascading-E expressions isn’t much better than the arrays; you’ll need to correctly sort out the hyper-operators and probably mess up a bunch of times!

Petossol

{10,10(5)2}

A 10^5 penteract of 10s. It requires solving multiple tesseracts, which in turn requires solving a mind-boggling number of cubes, and an even more mind-boggling number of squares, and rows, and we just can’t grasp how anyone would solve this! I suppose he still could, but at this point the computation is becoming abstract in itself.

Quinticahlah

E100#^#####100

Or E100#^#^#5. At last we reached the realm of #^#^#! Not too long to E100#^#^#100 anymore. You can guess what comes next...

Ectossol

{10,10(6)2}

A 10^6 hexeract of 10s! While we can draw tesseracts and penteracts quite eaily and still make them out, hexeracts and beyond will start to look like a mess even when mapped out by a computer program. The levels of decomposition needed to solve this are getting more and more horrendously huge.

Sexticahlah

E100#^#^#6

Zettossol

{10,10(7)2}

Septicahlah

E100#^#^#7

Yottossol

{10,10(8)2}

Octicahlah

E100#^#^#8

Ogdo-octicahlah

E100#^#^#98

This is Sbiis Saibian's 3000th googolism, defined using Cascading-E notation. It's approximately {10,100(8)(8)(8)(8)(8)(8)(8)(8)2} (8 (8)s) using Bowers' dimensional array notation.

Xennossol

{10,10(9)2}

Xenna- is one of the unofficial SI prefixes used for 1000^9, or an octillion. Bowers seems to like using this one.

Nonicahlah

E100#^#^#9

Dimendecal

{10,10(10)2} = 10^10 & 10

A 10-dimensional array of 10s! Solving this would require continuously going through hypercubes, back and forth as the array slowly decreases in complexity.

Decichlah

E100#^#^#10

Viginticahlah

E100#^#^#20

Nonaginticahlah

E100#^#^#90

Saibian defines more -cahlah numbers, but I’m skipping most of them because I don’t want to be repetitive. This is the last Saibianism smaller than the gongulus.

{10,10(100)2} = 10^100 & 10

A gongulus is an unspeakably huge number coined by Jonathan Bowers. It's a 100-dimensional array of tens, which has exactly a googol entries when the array is expanded out. Bowers seems to bring that number up a lot more than other numbers of his (see negative gongulus, part 1).

At this point, just to shake you up a little let's take a moment to discuss how INCREDIBLY HUGE a gongulus is. Tthis number makes Graham look adorable, to say the least. Graham’s number is so small that once you are introduced to it, you can explain it to anyone and they can understand how it would be computed! A gongulus, however, is far far beyond weeny little numbers whose computation you can understand. It’s much much much much much ... ... ... MUCH larger than Graham's number. A 100-dimensional cube may not seem too overwhelming, but once we get into it your mind will be blown.

To start off, a gongulus will look a bit like this:

x x x x x x x x x where each x is a 99-dimensional cube

And each 99-dimensional cube will consist of 10 98-dimensional cubes, and each of those will consist of 97-dimensional cubes, and each of THOSE will consist of 96-dimensional cubes, etc. The starting array for a gongulus will have a googol 10’s!

Still not impressed? Then let’s go inside the centeract (100-dimensional cube) and start seeing how it would be solved! First, you’ll need to solve the last 99-dimensional cube to turn the hypercube into an x*x*x*x.......*x*9 array of tens. But to solve that, you’ll need to solve a bunch of 98-dimensional cubes, and for each of those you’ll need to solve a bunch of 97-dimensional hypercubes, and for each one a 96-cube ... ... somewhere in the middle there’s 50, 49, 48, 47, etc. cubes ... ... until you get to the lines that decompose the squares, which in turn decompose the cubes, then the tesseracts ... each dimemsion would be more horrendous to solve than the previous! And that’s only the first 99-dimensional cube! Once you’ve got that 99-cube out of the way, you’ll need to solve the next incomprehensibly large 99-cube, but that would require solving lots and lots of 98-cubes, which requires a huge amount of 97-cubes, and a huge amount of 96-cubes, 95-cubes ... ... 29-cubes, 28-cubes ... ... tesseracts, cubes, squares, lines! Then the third 99-cube will need to be solved, and the fourth 99-cube next, each bigger than the previous, continuing with the fifth, sixth, seventh, eighth, ninth, and then the last 99-dimensional cube! To solve that cube, you’ll need a seemingly endless amount of 98-cubes, followed by 97, 96-, etc. cubes, but you’ve done that before a bunch of times, just this time it’s even bigger! Once you’re down to a 98-cube solve that to a 97-cube (which still  requires 96-, 95-, 94-cubes ... ... ... tesseracts, cubes, squares, lines)! Once that 97-cube is over and you have a 96-cube, you’ll need to continue and continue through 94 more dimensions until you get an insanely big planar array, and you’ll need to solve that until you get a very, very long linear array! You’ll ned to solve that into gradually smaller linear arrays, and then into an up-arrow notation where you’ll need to repetitively evaluate the expresssions until you finally get a huge power of 10! Evaluate that, and that is a gongulus! And that isn’t even the full picture! It seems to never come to an end when trying to solve, as Bowers says.

That long explanation above is much longer and more overwhelming than any explanation of Graham’s number! And a full explanation of Graham’s number is wimpy compared to this mind-boggling overview of the computation of a gongulus! The gongulus is much much too mighty for us mortals to comprehend. Yet it’s only the beginning of a series of much worse numbers! Eventually we won’t be able to even imagine anything of what the arrays would be like! In other words, the gongulus, as mighty as it is, is easily trumped by FAR more unfathomable numbers!

All in all, this number is a great example of a number that really crushes Graham's number - Sbiis Saibian describes the huge difference in a blog post, and suggests using a gongulus to replace the fame held by Graham's number, since Graham's number, by googological standards, is quite tiny and easy to analyze. Though I personally would transfer Graham's honor to something like the even bigger TREE(3), which like Graham's number has serious use in mathematics.

Second gongulus / Gonguxxus

{10,100(0,1)2} = {10,100(100)2} = 100^100 & 10

Bowers’ gongulus extensions (such as {10,100(0,3)2} or {10,100(0,0,0,0,1)2}) don’t really match the gongulus, since there’s no way to express a gongulus as {a,b(x,y)c}. To fix this problem, Aarex coins the second gongulus, which matches better with the extensions.

Sbiis Saibian calls this number gonguxxus continuing the goxxol, coloxxol, teroxxol, etc, idea.

Godgathor

E100#^#^#100

We’re all in all done with the godgahlah, gridgahlah, kubikahlah, and -icahlah series (collectively the godgahlah gang) and we’ve moved on to a whole new gang. Behold the godgathor gang. This Saibianism is comparable to the gongulus but closer to the second gongulus.

Even though #^#^# looks a lot friendlier than an x-dimensional array, guess what? It’s just as bad. Each #^#99 (#^####....#### with 99 #s) is equivalent to a 99-cube, each #^#98 is equal to a 98-cube, etc. Decomposing this will be quite akin to the horrendous decomposition of a gongulus!

Goober bunch

E100#^#101100

This irregular number was defined by Saibian to break the monotony of his numbers. It’s defined as E100#^#100*#^#100*#^#100......#^#100100 with 100 #^#100s, simplifying to the expression above.

Gongulusplex

{10,10(gongulus)2}

Remember the 100 dimensions we went through in the long gongulus paragraph? Now imagine having to go through a gongulus dimensions! We’ll pass through every whole number in this list up to a gongulus when working with the number of dimensions. Since you can’t even imagine how big a gongulus would be, it’s even more mind-boggling to imagine solving a gongulus-dimensional cube!

As impressive as this number is, it’s still a naive extension because anyone introduced to the gongulus could come up with that. We’ll need to move much faster than ANY recursion to get anywhere!

Grand godgathor

E100#^#^#100#2

Or E100#^#godgathor100. It looks absolutely amazing, but it’s the same situation as a gongulusplex.

Gibbering goober bunch

E100#^#goober bunch+1(goober bunch)

Defined as E100#^#goober bunch*#^#goober bunch#^#goober bunch......#^#goober bunch100 with a goober bunch #^#goober bunchs. It looks ambitious, but once again it isn’t a good improvement.

Gongulusduplex

{10,10(gongulusplex)2}

Just imagine......you’ll need to go through a gongulusplex dimensions to solve the number. Doing that and growing through such a gigantic number of dimensions brings a sense of vast darkness. Kinda creepy if your think about it.

Gongulustriplex

{10,10(gongulusduplex)2}

Gongulusquadriplex

{10,10(gongulustriplex)2}

Superdimensional Array Numbers 

{a,b(c)2}~{a,b((1)1)c} 

(order type w^w^w ~ w^w^w^w) 

Entries: 50

Gotrigathor

E100#^#^#100#^#^#100

Notice how we’re skipping stuff like E100#^#^#100##100 and heading straight to the good stuff.

Also, superdimensional arrays are arrays which have dimensions of dimensions. It’s the first level of tetrational arrays. Following are trimensions (dimensions of superdimensions) and quadramensions, which are the higher tetrational arrays.

Deutero-godgathor

E100#^#^#*#^#^#100

Or E100#^(#^#*#)2.

Trito-godgathor

E100#^#^#*#^#^#*#^#^#100

Or E100#^(#^#*#)3.

Hecato-godgathor / Godgathorfact

E100#^(#^#*#)100

Note that E100#^#^#*#^#^#*#^#^#*#^#^#......*#^#^#100 with 100 #^#^#s is NOT E100#^#^##100. It simplifies to only E100#^(#^#*#)100 .

Godgridgathor / Godgathordeuterfect

E100#^(#^#*##)100

Decomposes to E100#^(#^#*#)*#^(#^#*#)*#^(#^#*#)*......#^(#^#*#)100, with 100 #^(#^#*#)s. Just imagine how many multiplication strings you’ll need to go through to decompose that.

Dulatri

{3,3(0,2)2}

This Bowersism serves to help us better understand superdimensional arrays. To picture this array, imagine a 3x3x3 cube, but with each of the 27 slots filled with a 3x3x3 cube of 3’s, making it a number that scratches the surface of tetrational arrays. It’s also equal to an X^2X array of 3’s, with 729 threes.

Godcubicgathor / Godgathortritofact

E100#^(#^#*###)100

Godquarticgathor / Godgathortetrifact

E100#^(#^#*####)100

Gingulus

{10,100(0,2)2}

A 100^(2*100) array of 10’s. This is the first group of superdimensions. To solve visualize this array, imagine a 100^100 dimensional array, but each slot is filled with a gongulus array. The array has 10^400 entries in total.

Godgathordeus

E100#^(#^#*#^#)100

Comparable to the gingulus. We’re almost to E100#^#^##100! Also, we can define the hecato-godgathordeus, and godgrid-, -cubic-, and -quarticgathordeus.

Gangulus

{10,100(0,3)2}

A 100^(3*100) array of 10’s. The array can be visualized as a gongulus array of ginguluses.

Godgathortruce

E100#^(#^#*#^#*#^#)100

Simplifies to E100#^(#^##)3, or just E100#^#^##3. Comparable to gangulus.

Geengulus

{10,100(0,4)2}

Godgathorquad

E100#^#^##4

Gowngulus

{10,100(0,5)2}

Godgathorquid

E100#^#^##5

Gungulus

{10,100(0,6)2}

Godgathorsid

E100#^#^##6

Godgathorseptuce

E100#^#^##7

Godgathoroctuce

E100#^#^##8 

Godgathornonice

E100#^#^##9

Godgathordecice

E100#^#^##10

Bongulus

{10,100(0,0,1)2}

Or {10,100(0,100)2}. A 100^100^2 array of 10’s, but still a low level superdimensional array. If stage 1 is the second gongulus, stage 2 is the gingulus, stage 3 is the gangulus, stage 4 is the geengulus, etc, then this is stage 100.

Gralgathor

E100#^#^##100

Here’s a really epic number, comparable to bongulus. This number simplifies to E100#^(#^#*#^#*#^#*#^#*#^#......#^#)100 with 100 #^#s! To simplify it, you would start off with E100#^(#^#*#^#*#^#........*#100)100, which first decomposes to E100#^(#^#*#^#*#^#........*#99)*#^(#^#*#^#*#^#........*#99)*#^(#^#*#^#*#^#........*#99).......*#^(#^#*#^#*#^#........*#99)100 with 100 #^(#^#*#^#*#^#........*#99)s! The last (but ONLY the last) #^(#^#*#^#*#^#........*#99) decomposes to #^(#^#*#^#*#^#........*#98*#^(#^#*#^#*#^#........*#98)*#^(#^#*#^#*#^#........*#98)....*#^(#^#*#^#*#^#........*#98), then the last one of those decomposes to #^(#^#*#^#*#^#........*#97*#^(#^#*#^#*#^#........*#97)*#^(#^#*#^#*#^#........*#97)....*#^(#^#*#^#*#^#........*#97), then we'll have to repeat the process 97 more times to end with a #^(#^#*#^#*#^#*#^#.....*#^#) with 99 #^#s instead of 100. Right then, we can decompose that very last #^# to #100 ... just so we can repeat that whole process all over again. Then we have to repeat it 100 times until it ends with a ridiculously long product of delimiters, but then we'll need to decompose that, and repeat again, and decompose that, repeat again ... you can scream now ...

Absolutely mind-boggling!!!! And the godgathor (and gongulus) seemed mighty just moments ago. They are now in the dust with the wimpy little grand godgahlahgong! I told you numbers that make the gongulus look wimpy are headed our way - but you ain't seen nothing yet!

Graltrigathor

E100#^#^##100#^#^##100

Deutero-gralgathor

E100#^#^##*#^#^##100

Or E100#^(#^##*#)2.

Hecato-gralgathor

E100#^(#^##*#)100

Hecato-x is no longer very effective. We’re going much faster now.

Gralgridgathor

E100#^(#^##*##)100

Decomposes to E100@100@100@100.......@100 where each @ is #^(#^##*#).

Gralcubicgathor

E100#^(#^##*###)100

Gralgodgathgathor

E100#^(#^##*#^#)100

Gralgodgathordeusgathor

E100#^(#^##*#^#*#^#)100

Bingulus

{10,100(0,0,2)2}

An X^(2*X^2) array of 10s. To imagine this array, you'll need a bongulus array of bongulus arrays - keep in mind that a bongulus array is a 100x nested array of gongulus arrays.

Gralgathordeus

E100#^(#^##*#^##)100

Or E100#^#^###2. Comparable to bingulus.

Trimentri

{3,3(0,0,0,1)2}

Remember megafuga-three, which was equivalent to about 7.6 trillion? Well, that number is used to define this number, specifically as a 3^3^3 or 3^^3 array of 3’s. Trimentri can be expressed in various other ways. Here they are:

{3,3(0,0,3)2}

{3,3((1)1)2}

A 3-superdimsional array of 3’s

A 1-trimensional array of 3’s

3^3^3&3

3^^3&3

3^^^2&3

A 3 tetrated to 3 array of 3’s

A 3 pentated to 2 array of 3’s

Bangulus

{10,100(0,0,3)2}

An X^(3*X^2) array of 10s.

Gralgathortruce

E100#^#^###3

Beengulus

{10,100(0,0,4)2}

We saw this number’s reciprocal a loooooooooong time ago in part 1.

Gralgathorquad

E100#^#^###4

Trongulus

{10,100(0,0,0,1)2}

In the lower superdimensional arrays but still super insane. This number is about an X^X^3 array of 10’s!

Thraelgathor

E100#^#^###100

The numbers just keep getting crazier. To compute this, you’ll need to follow the same general thing we did with the gralgathor, then do it again and this time even longer, and it's difficult to bring to words. Keep in mind that we can coin plenty of numbers based on this like an isosto-thraelgathor and a thraelgathorseptuce.

Quadrongulus

{10,100(0,0,0,1)2} 

A four-superdimensional array of tens.

Terinngathor

E100#^#^####100

Comparable to the quadrongulus.

Pentaelgathor

E100#^#^#####100

Hexaelgathor

E100#^#^#^#6

Heptaelgathor

E100#^#^#^#7

Octaelgathor

E100#^#^#^#8 

Ennaelgathor

E100#^#^#^#9

Dekaelgathor

E100#^#^#^#10

Goplexulus

{10,100((1)1)2}

Also imaginable as:

{10,100(0,0,0,0.......0,1)2} with 100 zeros

100^100^100&10

A 100-superdimensional array of tens

A 100 tetrated to 3 array of tens

This number is right around the end of superdimensional arrays and the beginning of higher tetrational arrays. It's formed with some pretty insane array nesting.

Godtothol

E100#^#^#^#100

This number simplifies to E100#^#^#100100 (hectaelgathor perhaps), and once solving it further the expression expands rapidly in length. We saw how insane the gralgathor was, so this has to be much much more crazy. By the way, this is comparable to goplexulus.

The Ordinal-Tetration Range

{a,b(x,y.....n)c} ~ X^^X & a

(order type w^w^w^w ~ ε0)

Entries: 22

Graltothol

E100#^#^#^##100

The gralgathor was crazy, so is there a reason for this not to be super ultra mega crazy? I think not. To solve this, you’ll need to first go through the whole gralgathor fun zillions of times just to get anywhere. This is about an X^X^X^2, or 2-trimensional, array of tens!!

Hyper-gralgodgathorseptucegathor

E100#^#^(#^##*#^##)7

This is Sbiis Saibian's 4000th googolism, defined using Cascading-E notation. It's a member of the graltothol squadron in the godtothol regiment. Using Bowers' tetrational array notation this is about {10,100((2)(1)(1)(1)(1)(1)(1)(1)1)2}, and using the fast-growing hierarchy it's approximately fw^w^w^(w^2*w7)(100). Read Sbiis Saibian's list of Cascading-E googolisms for why it's named like that.

Thraeltothol

E100#^#^#^###100

Terinntothol

E100#^#^#^####100

Goduplexulus

{10,10((100)1)2} = 100^^4 & 10

We’re heading further and further into the tetrational arrays - this is a 100-trimensional array of tens.

Godtertol

E100#^#^#^#^#100

We’re almost done with the Cascading-E numbers and are getting ready to head into Extended Cascading-E. This is comparable to goduplexulus. I could include all the numbers in the godtertathol gang and the rest of the -tathol gangs, but I don’t want to be repetitive.

Gotriplexulus

100^^5 & 10 = {10,100(((1)1)1)2}

A 100-quadramensional array of tens.

Godtopol

E100#^#^#^#^#^#100

With these insane numbers, it may be tricky to remember that we're blasting through them at light speed, a lot faster than we could - actually we're going WAY FASTER than light speed through these monsters!

Godgahlah-carta-tethrathoth

E100#^^#100#^#100

Gridgahlah-carta-tethrathoth

E100#^^#100#^##100

Kubikahlah-carta-tethrathoth

E100#^^#100#^###100

Quarticahlah-carta-tethrathoth

E100#^^#100#^####100

Godgathor-carta-tethrathoth

E100#^^#100#^#^#100

Godtothol-carta-tethrathoth

E100#^^#100#^#^#^#100

Tethrathoth-carta-tethrathoth/tethratrithoth

E100#^^#100#^^#100 = E100#^^#*#3

Tethraterthoth

E100#^^#100#^^#100#^^#100 = E100#^^#*#4

Tethrathoth-by-hyperion

E100#^^#*#100

Tethrathoth-by-deutrohyperion

E100#^^#*##100

Evaluates to E100#^^#*#100#^^#*#100.....#^^#*#100 with 100 100’s.

Tethrathoth-by-tritohyperion

E100#^^#*###100

Tethrathoth-by-godgahlah

E100#^^#*#^#100

Tethrathoth-by-godgathor

E100#^^#*#^#^#100

Deutero-tethrathoth

E100#^^#*#^^#100 = E100(#^^#)^#2

Trito-tethrathoth

E100#^^#*#^^#*#^^#100 = E100(#^^#)^#3

Hecato-tethrathoth/tethrafact

E100(#^^#)^#100

This number is called tethrafact because the tethrathoth delimiter is the only factor of the whole expression. It’s still not really that great of an improvement, but kind of the base for what will come.

Grideutertethrathoth

E100(#^^#)^##100

Or E100(#^^#)^#*(#^^#)^#*(#^^#)^#.....*(#^^#)^# with 100 (#^^#)^#s. This number can also be called hecato-tethrafact, but Saibian does not give this name.

Kubicutethrathoth

E100(#^^#)^###100 = E100(#^^#)^#^#3

Tethragodgathor / Centicutethrathoth

E100(#^^#)^#^#100

Tethragodtothol

E100(#^^#)^#^#^#100 = E100(#^^#)^(#^^#)3

Tethraduliath/tethra-tethrathoth/tethrathoth-dopplux/tethrathoth-dubletetrate

E100(#^^#)^(#^^#)100 = E100(#^^#)^^#2

This is a milestone point in Extended Cascading-E - it's just starting on tetrating the tethrathoth delimiter. Pretty soon the tetration will be iterated. It's interesting to point out that Saibian explicity gives four different names for this number.

Tethradulifact

E100(#^^#)^(#^^#*#)100

Evaluates to E100(#^^#)^(#^^#)*(#^^#)^(#^^#)*(#^^#)^(#^^#).....*(#^^#)^(#^^#) with 100 (#^^#)^(#^^#)s.

Grideutertethraduliath

E100(#^^#)^(#^^#*##)100

Tethraduli-godgathor

E100(#^^#)^(#^^#*#^#)100

Tethrathruliath

E100(#^^#)^(#^^#*#^^#)100

Tethraterliath

E100(#^^#)^(#^^#*#^^#*#^^#)100 = E100(#^^#)^(#^^#)^#3

Monster-Giant

E100(#^^#)^(#^^#)^#100

The somewhat irregular Monster-Giant is a pretty awesome number. It decomposes to E100(#^^#)^(#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#)100.

This is pretty insane now (comparable to a (X^^X)X array), but only starting a whole new realm of insanity.

Grand Monster-Giant

E100(#^^#)^(#^^#)^#100#2

Or E100(#^^#)^(#^^#*#^^#*#^^#*#^^#*#^^#*......................*#^^#)100 with Monster-Giant+1 #^^#s! As impressive as this sounds, it's still a naive extensions. We can further extend upon the Monster-Giant with numbers like:

Deutero-Monster-Giant

E100(#^^#)^(#^^#)^#*(#^^#)^(#^^#)^#100

Trito-Monster-Giant

E100(#^^#)^((#^^#)^#*#)3

Hecato-Monster-Giant

E100(#^^#)^((#^^#)^#*#)100

Tethra-Monster-Giant

E100(#^^#)^((#^^#)^#*#^^#)100

Tethraduli-Monster-Giant

E100(#^^#)^((#^^#)^#*#^^#*#^^#)100 = E100(#^^#)^((#^^#)^#*(#^^#)^#)2

Monster-Monster-Giant = Two-ex-Monster-Giant

E100(#^^#)^((#^^#)^#*(#^^#)^#)100 = E100(#^^#)^(#^^#)^##2

Three-ex-Monster-Giant

E100(#^^#)^((#^^#)^#*(#^^#)^#*(#^^#)^#)100 = E100(#^^#)^(#^^#)^##3

Hundred-ex-Monster-Giant/Monster-Grid

E100(#^^#)^(#^^#)^##100

Monster-Giant-ex-Monster-Giant

E100(#^^#)^(#^^#)^##(Monster-Giant)

Grand Monster-Grid

E100(#^^#)^(#^^#)^##100#2

Monster-Cube

E100(#^^#)^(#^^#)^###100

Monster-Tesseract

E100(#^^#)^(#^^#)^####100

Monster-Hecateract

E100(#^^#)^(#^^#)^#^#100

Tethrathoth-trebletetrate

E100(#^^#)^(#^^#)^(#^^#)100 = E100(#^^#)^^#3

Super Monster-Giant

E100(#^^#)^(#^^#)^(#^^#)^#100

Evaluates to:

E100(#^^#)^(#^^#)^(#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*

#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#*#^^#)100

Super Monster-Grid

E100(#^^#)^(#^^#)^(#^^#)^##100

Tethrathoth-quadrupletetrate

E100(#^^#)^^#4

Tethrathoth-quintupletetrate

E100(#^^#)^^#5

Tethrathoth-decupletetrate

E100(#^^#)^^#10

Terrible tethrathoth

E100(#^^#)^^#100

Evaluates to E100(#^^#)^(#^^#)^(#^^#)^(#^^#)^(#^^#).......^(#^^#) with 100 (#^^#)s.

Dubletetrated terrible tethrathoth

E100((#^^#)^^#)^((#^^#)^^#)100 = E100(((#^^#)^^#)^^#)2

Trebletetrated terrible tethrathoth

E100(((#^^#)^^#)^^#)3

Double-terrible tethrathoth

E100(((#^^#)^^#)^^#)100

Triple-terrible tethrathoth

E100((((#^^#)^^#)^^#)^^#)100

The Hyper-Epsilon Range

X^^(X+1) & a - X^^X^2 & a

(order type εw ~ ζ0)

Entries: 68

Tethriterator / Tethrathoth ba’al / 99-ex-terrible tethrathoth

E100(....((#^^#)^^#)........^^#)100 with 100 #^^#s = E100#^^#>#100

This is Sbiis Saibian's smallest googolism to use the > operator, a special operator called the "caret top" which iterates the function applied to the # before it. Terrible tethrathoth is E100#^^#>#2, double-terrible tethrathoth is E100#^^#>#3, triple-terrible tethrathoth is E100#^^#>#4, and so on with the > operator.

This number called tethriterator because it iterates the smallest tetrational delimiter, or #^^#.

Grand tethriterator / Great and Terrible Tethrathoth / tethrathoth-ba'al-minus-one-ex-terrible tethrathoth

E100(... ...((#^^#)^^#)^^#)^^#) ... ... ^^#)100 with tethrathoth ba’al #^^#s = E100#^^#>#100#2

As insane as this looks, you should know by now that such recursion, unfortunately, is not really progress anymore.

Quadrule-tetrated-tethrathoth-ex-terrible tethrathoth

E100#^^#>#(1+E100(#^^#)^(#^^#)^(#^^#)^(#^^#)100)

This is Sbiis Saibian's 6000th googolism, defined using Extended Cascading-E. It's about fεw(fε0^ε0^ε0^ε0(100)) using the fast-growing hierarchy, or about X^^(X+1) & ((X^^X)^^4 & 100) using the climbing method interpretation of the array-of operator in BEAF. It's an example of a number you can form by repeatedly applying the terrible operator, but it's much smaller than even...

Grangol-carta-tethriterator

E100#^^#>#100#100

Or 99-ex-grand tethriterator. Although this is mind-crushingly larger than something like Great-and-Terrible-Tethrathoth-ex-terrible tethrathoth, it's not really progress. Let's jump to:

Tethritertri

E100#^^#>#100#^^#>#100 = E100#^^#>#*#3

Tethriterhecate/tethritera-by-hyperion

E100#^^#>#*#100

Tethritera-by-deutero-hyperion

E100#^^#>#*##100

Tethritera-by-godgahlah

E100#^^#>#*#^#100

Tethritera-by-tethrathoth

E100#^^#>#*#^^#100

Deutero-tethriterator

E100#^^#>#*#^^#>#100

Trito-tethriterator

E100#^^#>#*#^^#>#*#^^#>#100 = E100(#^^#>#)^#3

Hecato-tethriterator/tethriterfact

E100(#^^#>#)^#100

Grideutertethriterator/hecato-tethriterfact

E100(#^^#>#)^##100

Tethriter-godgathor

E100(#^^#>#)^#^#100

Tethriter-tethrathoth

E100(#^^#>#)^#^^#100

Tethriter-terri-tethrathoth

E100(#^^#>#)^(#^^#)^^#100

Tethriter-dubletetrate

E100(#^^#>#)^(#^^#>#)100 = E100(#^^#>#)^^#2

Terrible tethriterator

E100(#^^#>#)^^#100

Double-terrible tethriterator

E100((#^^#>#)^^#)^^#100

Tethriditerator / 100-ex-terrible tethriterator

E100#^^#>(#+#)100

Terrible tethriditerator

E100(#^^#>(#+#))^^#100

Tethritriterator / 100-ex-terrible tethritriterator

E100#^^#>(#+#+#)100 = E100#^^#>##3

Tethriquaditerator

E100#^^#>##4

Tethrigriditerator

E100#^^#>##100

Tethricubiculator

E100#^^#>###100

Tethriquarticulator

E100#^^#>####100

Tethrispatialator

E100#^^#>#^#100

Tethrispatial-squarediterator

E100#^^#>(#^#*#^#)100

Tethrispatial-cubiculator

E100#^^#>#^##3

Tethrideuterspatialator

E100#^^#>#^##100

Tethritritospatialator

E100#^^#>#^###100

Tethritetertospatialator

E100#^^#>#^#^#4

Tethri-superspatialator

E100#^^#>#^#^#100

Tethri-quadratetratediterator

E100#^^#>#^#^#^#100

Dustaculated-tethrathoth

E100#^^#>#^^#100

Can also be written as E100#^^##2.

Gippatoth

X^^2X & 100

This is a googolism I coined as a fairly low-level pentational array number. I'm putting this and related numbers under the climbing method interpretation - although the non-climbing interpretation is more commonly used among the googology community, the climbing method intentionally matches nicely with Extended Cascading-E, and is largely advocated by Bowers. This is comparable to a dustaculated-tethrathoth.

Tethriter-turreted-tethrathoth

E100#^^#>#^^#>#100

Territethriter-turreted-tethrathoth

E100#^^#>(#^^#>#)^^#100

Not to be confused with the much smaller terrible tethriter-turreted-tethrathoth.

Tethriditer-turreted-tethrathoth

E100#^^#>#^^#>(#+#)100

Tethritriter-turreted-tethrathoth

E100#^^#>#^^#>##3

Tethrigriditer-turreted-tethrathoth

E100#^^#>#^^#>##100

Tristaculated-tethrathoth

E100#^^#>#^^#>#^^#100

Gappatoth

X^^3X & 100

Comparable to a tristaculated-tethrathoth.

Tetrastaculated-tethrathoth

E100#^^#>#^^#>#^^#>#^^#100

Geepatoth

X^^4X & 100

Pentastaculated-tethrathoth

E100#^^##5

Dekastaculated-tethrathoth

E100#^^##10

Tethracross / Tethrasquare

E100#^^##100

A tethracross is another one of Sbiis Saibian's milestone googolisms. It's on the order of zeta-zero in the fast-growing hierarchy. It evaluates to:

E100#^^#>#^^#>#^^# ... ... ... >#^^#>#^^#100 with 100 copies of #^^#

It is comparable to Bowers' kungulus using the more common interpretation of pentational arrays, although using the climbing method (which I'm using on this list) it's much smaller than a kungulus.

Boppatoth

X^^X^2 & 100

Another extrapolation from the tethrathoth, based on Bowers' number, the bongulus. It's comparable to a tethrasquare.

Giaquixul

200![200,200,200,200,200]

A number I coined, which is in the realm of X^^X^2 arrays. The next HAN number after this will be the hugexul.

Berlin Wall

E100#^^##100,000,000

An irregular number defined by Saibian. The expression it expands to, or E100#^^#>#^^#>#^^#>#^^#.....#^^#>#^^#>#^^#100 with 100,000,000 #^^#>s wouldn’t be much longer than the real Berlin Wall, but that also depends on the text size.

Grand tethracross

E100#^^##100#2

Grand Berlin Wall

E100#^^##100,000,000#2

~ fζ0+1(63)

Fish number 6 is the largest computable Fish number, defined by Kyodaisuu of Googology Wiki in 2007. It extends upon Fish number 5's system with a two-argument function that reaches zeta-0 in the fast growing hierarchy (the power of X^^X^2 arrays), so it falls just under a grangol-carta-tethrasquare, equal to about fζ0+1(100)

The Zeta-Eta Range

X^^^X^2 & a - X^^X^X & a

(order type ζ0 ~ φ(w,0))

Entries: 121

Grangol-carta-tethrasquare

E100#^^##100#100

Godgahlah-carta-tethrasquare

E100#^^##100#^#100

Tethrathoth-carta-tethrasquare

E100#^^##100#^^#100

Tethriterator-carta-tethrasquare

E100#^^##100#^^#>#100

Tethrasquare-by-deuteron

E100#^^##100#^^##100

Tethrasquare-by-triton

E100#^^##100#^^##100#^^##100 = E100#^^##*#4

Tethrasquare-by-hyperion

E100#^^##*#100

Tethrasquare-by-deuterohyperion

E100#^^##*##100

Tethrasquare-by-godgahlah

E100#^^##*#^#100

Tethrasquare-by-tethrathoth

E100#^^##*#^^#100

Tethrasquare-by-tethriterator

E100#^^##*#^^#>#100

Deutero-tethrasquare

E100#^^##*#^^##100

Trito-tehtrasquare

E100#^^##*#^^##*#^^##100 = E100(#^^##)^#3

Hecato-tethrasquare/tethrasquarorfact

E100(#^^##)^#100

Grideutertethrasquare

E100(#^^##)^##100

Centicutethrasquare

E100(#^^##)^#^#100

E100(#^^##)^#^#^#100

E100(#^^##)^(#^^#)100

E100(#^^##)^(#^^#>#)100

Dutetrated-tethrasquare

E100(#^^##)^(#^^##)100

Tritetrated-tethrasquare

E100(#^^##)^(#^^##)^(#^^##)100 = E100(#^^##)^^#3

Terrible tethrasquare

E100(#^^##)^^#100

Tethriterated-tethrasquare

E100(#^^##)^^#>#100

Tethrastaculated-tethritertethrasquare

E100(#^^##)^^#>#^^#100

Tethriterstaculated-tethritertethrasquare

E100(#^^##)^^#>#^^#>#100

Dustaculated-tethraturreted-tethritertethrasquare

E100(#^^##)^^#>#^^#>#^^#100

Tristaculated-tethraturreted-tethritertethrasquare

E100(#^^##)^^#>#^^#>#^^#>#^^#100 = E100(#^^##)^^#>#^^##3

Tetrastaculated-tethraturreted-tethritertethrasquare

E100(#^^##)^^#>#^^##4

Tethrasquare-turreted-tethritertethrasquare

E100(#^^##)^^#>#^^##100

Territethrasquare-turreted-tethritetrtethrasquare / Dustaculated-tethritertethrasquare

E100(#^^##)^^#>(#^^##)^^#100

Sorry that the names sound absurdly long, but it kind of needs to be that way if we want to have a useful system to name any such number. After all, naming systems are a big part of googology, and almost by necessity the names can get pretty long.

Tristaculated-tethritertethrasquare

E100(#^^##)^^#>(#^^##)^^#>(#^^##)^^#100 = E100(#^^##)^^##3

Tetrastaculated-tethritertethrasquare

E100(#^^##)^^##4

Dekastaculated-tethritertethrasquare

E100(#^^##)^^##10

Secundo-tethrated tethrasquare

E100(#^^##)^^##100

Dustaculated-secundo-tethrated tethrasquare

E100(#^^##)^^##>(#^^##)^^##100

Tristaculated-secundo-tethrated tethrasquare

E100(#^^##)^^##>(#^^##)^^##>(#^^##)^^##100 = E100((#^^##)^^##)^^##3

Thrice-tethrasecunda

E100((#^^##)^^##)^^##100 = E100#^^##>#3

Quatrice-tethrasecunda

E100#^^##>#4

Tethrasquarediterator

E100#^^##>#100

Tethrasquared-diterator

E100#^^##>(#+#)100 = E100#^^##>##2

Tethrasquared-triterator

E100#^^##>##3

Tethrasquared-griditerator

E100#^^##>##100

Tethrasquared-cubiculator

E100#^^##>###100

Tethrasquared-spatialator

E100#^^##>#^#100

Tethrasquared-superspatialator

E100#^^##>#^#^#100

Tethrasquared-quadratetratediterator

E100#^^##>#^^#4

Tethraturreted-tethrasquare

E100#^^##>#^^#100

Dustacu-tethraturreted-tethrasquare

E100#^^##>#^^#>#^^#100

Tristacu-tethraturreted-tethrasquare

E100#^^##>#^^#>#^^#>#^^#100 = E100#^^##>#^^##3

Dustaculated-tethrasquare

E100#^^##>#^^##100

Tristaculated-tethrasquare

E100#^^##>#^^##>#^^##100 = E100#^^###3

Tetrastaculated-tethrasquare

E100#^^###4

Dekastaculated-tethrasquare

E100#^^###10

Tethracubor / tethratertia

E100#^^###100

A tethracubor is of the order of eta-zero in the fast-growing hierarchy. It's the next of Sbiis Saibian's milestone googolisms, and its name begins the idea of naming numbers after multidimensional figures.

Troppatoth

X^^X^3 & 100

Comparable to tethracubor.

Grand tethracubor

E100#^^###100#2 = E100#^^###tethracubor

Deutero-tethracubor

E100#^^###*#^^###100

Hecato-tethracubor/tethracuborfact

E100(#^^###)^#100

Grideutertethracubor

E100(#^^###)^##100

Tethracubor-godgathored

E100(#^^###)^#^#100

Tethracubor-godtotholed

E100(#^^###)^#^#^#100

Tethracubor-isptethrathoth

E100(#^^###)^#^^#100

Tethracubor-isptethriterator

E100(#^^###)^#^^#>#100

Tethracubor-isptethrasquaror

E100(#^^###)^#^^##100

Dutetrated-tethracubor

E100(#^^###)^(#^^###)100

Tritetrated-tethracubor

E100(#^^###)^(#^^###)^(#^^###)100 = E100(#^^###)^^#3

Terrible tethracubor

E100(#^^###)^^#100

Terrible terrible tethracubor

E100((#^^###)^^#)^^#100 = E100(#^^##)^^#>#2

Tethritertethracubor

E100(#^^###)^^#>#100

Dustaculated-territethracubor

E100(#^^###)^^#>(#^^###)^^#100

Tristaculated-tethracubor

E100(#^^###)^^#>(#^^###)^^#>(#^^###)^^#100 = E100(#^^###)^^##3

Terrisquared-tethracubor

E100(#^^###)^^##100

Territerated terrisquared-tethracubor

E100((#^^###)^^##>#100

Double-terrisquared-tethracubor

E100((#^^###)^^##)^^##100

Triple-terrisquared-tethracubor

E100(((#^^###)^^##)^^##)^^##100 = E100(#^^###)^^##>#3

Terrisquarediter-tethracubor

E100(#^^###)^^##>#100

Dustaculated-terrisquared-tethracubor

E100(#^^###)^^##>(#^^###)^^##100

Tristaculated-terrisquared-tethracubor

E100(#^^###)^^##>(#^^###)^^##>(#^^###)^^## = E100(#^^###)^^###3

Tethraducubor

E100(#^^###)^^###100

Tethratricubor

E100((#^^###)^^###)^^###100

Tethratetracubor

E100(((#^^###)^^###)^^###)^^###100 = E100#^^###>#4

Tethracubiter

E100#^^###>#100

Tethracubor-diterator

E100#^^###>(#+#)100 = E100#^^###>##2

Tethracubo-gridulator

E100#^^###>##100

Dustaculated-tethracubor

E100#^^###>#^^###100

Tristaculated-tethracubor

E100#^^####3

Tethrateron

E100#^^####100

Now we reach a bit of trouble in naming the numbers. What should we call this? An obvious choice seems to be tethratesseract, but that’s too long. 4-dimensional figures are often called polychorons, so another choice would be tethrapolychoron, but that’s also too long. The name "polychoron" litterally means "many rooms" and polychorons are composed of multiple 3-dimensional figures, so a "choron" can be considered to be a 3-D figure. Then we can take the word “polyteron”, which is a 5-dimensional figure. We can extract the root “teron” from there and use the convenient name “tethrateron”. This is also convenient because the name “teron” directly implies four.

Quadroppatoth

X^^X^4 & 100

Comparable to tethrateron.

Tethrateron-by-deuteron

E100#^^####100#^^######100