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The gargantuul regiment is a series of numbers from E100#100#100#100#100#100#100#100#100 to E1#1#1#1#1#1#1#1#1#10,000 defined using Hyper-E Notation (i.e. beginning from gargantuul and up to myria-endekaxis).[1] The numbers were coined by Sbiis Saibian.

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List of numbers of the regiment

Name of number Hyper-E Notation (definition) Arrow notation (approximation)
gargantuul E100#100#100#100#100#100#100#100#100 \(10\uparrow^9 100\)
ginorgolennex E100#100#100#100#100#100#100#100#1#2 \(10\uparrow^9 (10\uparrow^8 100)\)
ginorgoloctexiennex E100#100#100#100#100#100#100#100#2#2 \(10\uparrow^9 (10\uparrow^8 (10\uparrow^8 100))\)
ginorgolduoctexiennex E100#100#100#100#100#100#100#100#3#2 \(10\uparrow^9 (10\uparrow^8 (10\uparrow^8 (10\uparrow^8 100)))\)
gargantuulennex E100#100#100#100#100#100#100#100#100#2 \(10\uparrow^9 (10\uparrow^9 100)\)
ginorgolduennex E100#100#100#100#100#100#100#100#1#3 \(10\uparrow^9 (10\uparrow^9 (10\uparrow^8 100))\)
ginorgoloctexiduennex E100#100#100#100#100#100#100#100#2#3 \(10\uparrow^9 (10\uparrow^9 (10\uparrow^8 (10\uparrow^8 100)))\)
ginorgolduoctexiduennex E100#100#100#100#100#100#100#100#3#3 \(10\uparrow^9 (10\uparrow^9 (10\uparrow^8 (10\uparrow^8 (10\uparrow^8 100))))\)
gargantuulduennex E100#100#100#100#100#100#100#100#100#3 \(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 100))\)
gargantuulchime E1000#1000#1000#1000#1000#1000#1000#1000#1000 \(10\uparrow^9 1000\)
gargantuulennexichime E1000#1000#1000#1000#1000#1000#1000#1000#1000#2 \(10\uparrow^9 (10\uparrow^9 1000)\)
gargantuulennexichime E1000#1000#1000#1000#1000#1000#1000#1000#1000#3 \(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 1000))\)
gargantuultoll E10,000#10,000#10,000#10,000#10,000#

10,000#10,000#10,000#10,000

\(10\uparrow^9 10^4\)
gargantuulennexitoll E10,000#10,000#10,000#10,000#10,000#

10,000#10,000#10,000#10,000#2

\(10\uparrow^9 (10\uparrow^9 10^4)\)
gargantuulduennexitoll E10,000#10,000#10,000#10,000#10,000#

10,000#10,000#10,000#10,000#3

\(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 10^4))\)
gargantuulgong E100,000#100,000#100,000#100,000#100,000#

100,000#100,000#100,000#100,000

\(10\uparrow^9 10^5\)
gargantuulennexigong E100,000#100,000#100,000#100,000#100,000#

100,000#100,000#100,000#100,000#2

\(10\uparrow^9 (10\uparrow^9 10^5)\)
gargantuulduennexigong E100,000#100,000#100,000#100,000#100,000#

100,000#100,000#100,000#100,000#3

\(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 10^5))\)
gargantuulbong E100,000,000#100,000,000#100,000,000# ...

...100,000,000#100,000,000#100,000,000 w/9 100,000,000s

\(10\uparrow^9 10^8\)
gargantuulennexibong E100,000,000#100,000,000#100,000,000# ...

... #100,000,000#100,000,000#100,000,000#2 w/9 100,000,000s

\(10\uparrow^9 (10\uparrow^9 10^8)\)
gargantuulduennexibong E100,000,000#100,000,000#100,000,000# ...

... #100,000,000#100,000,000#100,000,000#3 w/9 100,000,000s

\(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 10^8))\)
gargantuulthrong E100,000,000,000#100,000,000,000# ...

...#100,000,000,000#100,000,000,000 w/9 100,000,000,000s

\(10\uparrow^9 10^{11}\)
gargantuulennexithrong E100,000,000,000#100,000,000,000# ...

... #100,000,000,000#100,000,000,000#2 w/9 100,000,000,000s

\(10\uparrow^9 (10\uparrow^9 10^{11})\)
gargantuulduennexithrong E100,000,000,000#100,000,000,000# ...

... #100,000,000,000#100,000,000,000#3 w/9 100,000,000,000s

\(10\uparrow^9 (10\uparrow^9 (10\uparrow^9 10^{11}))\)
googolennex E100#1#1#1#1#1#1#1#1#2 \(10\uparrow^9 10^{100}\)
grangolennex E100#100#1#1#1#1#1#1#1#2 \(10\uparrow^9 (10 \uparrow^2 100)\)
greagolennex E100#100#100#1#1#1#1#1#1#2 \(10\uparrow^9 (10 \uparrow^3 100)\)
gigangolennex E100#100#100#100#1#1#1#1#1#2 \(10\uparrow^9 (10 \uparrow^4 100)\)
gorgegolennex E100#100#100#100#100#1#1#1#1#2 \(10\uparrow^9 (10 \uparrow^5 100)\)
gulgolennex E100#100#100#100#100#100#1#1#1#2 \(10\uparrow^9 (10 \uparrow^6 100)\)
gaspgolennex E100#100#100#100#100#100#100#1#1#2 \(10\uparrow^9 (10 \uparrow^7 100)\)
gargantuulplex E(E100#100#100#100#100#100#100#100#100) \(10\uparrow (10 \uparrow^9 100)\)
gargantuuldex E100#(E100#100#100#100#100#100#100#100#100) \(10\uparrow^2 (10 \uparrow^9 100)\)
gargantuulthrex E100#100#

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

\(10\uparrow^3 (10 \uparrow^9 100)\)
gargantuultetrex E100#100#100#

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

\(10\uparrow^4 (10 \uparrow^9 100)\)
gargantuulpentex E100#100#100#100#

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

\(10\uparrow^5 (10 \uparrow^9 100)\)
gargantuulhex E100#100#100#100#100#

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

\(10\uparrow^6 (10 \uparrow^9 100)\)
gargantuulheptex E100#100#100#100#100#100#

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

\(10\uparrow^7 (10 \uparrow^9 100)\)
gargantuuloctex E100#100#100#100#100#100#100#

(E100#100#100#100#100#100#100#100#100) = E100#100#100#100#100#100#100#100#101

\(10\uparrow^8 (10 \uparrow^9 100)\)
ecetonennex E303#1#1#1#1#1#1#1#1#2 \(10 \uparrow^9 10^{303}\)
ecetonduennex E303#1#1#1#1#1#1#1#1#3 \(10 \uparrow^9 (10 \uparrow^9 10^{303})\)
tria-endekaxis E1#1#1#1#1#1#1#1#1#3 \(10 \uparrow^{10} 3\)
tetra-endekaxis E1#1#1#1#1#1#1#1#1#4 \(10 \uparrow^{10} 4\)
deka-endekaxis E1#1#1#1#1#1#1#1#1#10 \(10 \uparrow^{10} 10\)
hecta-endekaxis E1#1#1#1#1#1#1#1#1#100 \(10 \uparrow^{10} 100\)
chilia-endekaxis E1#1#1#1#1#1#1#1#1#1000 \(10 \uparrow^{10} 1000\)
myria-endekaxis E1#1#1#1#1#1#1#1#1#10,000 \(10 \uparrow^{10} 10000\)

Sources

1. Sbiis Saibian, 4.3.2 - Hyper-E Numbers