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

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Gorgegol regiment Gaspgol regiment

## List of numbers of the regiment

Name of number Hyper-E Notation (definition) Arrow notation (approximation)
gulgol E100#100#100#100#100#100 \(10 \uparrow^6 100\)
gorgegolhex E100#100#100#100#100#1#2 \(10 \uparrow^6 (10 \uparrow^5 100)\)
gorgegolpentexihex E100#100#100#100#100#2#2 \(10 \uparrow^6 (10 \uparrow^5 (10\uparrow^5 100))\)
gulgolhex E100#100#100#100#100#100#2 \(10 \uparrow^6 (10\uparrow^6 100)\)
gorgegolduhex E100#100#100#100#100#1#3 \(10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^5 100))\)
gorgegolpentexiduhex E100#100#100#100#100#2#3 \(10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^5 (10 \uparrow^5 100)))\)
gulgolduhex E100#100#100#100#100#100#3 \(10 \uparrow^6 (10\uparrow^6 (10\uparrow^6 100))\)
gorgegoltrihex E100#100#100#100#100#1#4 \(10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^5 100)))\)
gorgegolpentexitrihex E100#100#100#100#100#2#4 \(10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^5 (10 \uparrow^5 100))))\)
gulgoltrihex E100#100#100#100#100#100#4 \(10 \uparrow^6 (10 \uparrow^6 (10\uparrow^6 (10\uparrow^6 100)))\)
gulgolchime E1000#1000#1000#1000#1000#1000 \(10 \uparrow^6 1000\)
gulgolhexichime E1000#1000#1000#1000#1000#1000#2 \(10 \uparrow^6 (10 \uparrow^6 1000)\)
gulgolduhexichime E1000#1000#1000#1000#1000#1000#3 \(10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^6 1000))\)
gulgoltoll E10,000#10,000#10,000#10,000#10,000#10,000 \(10 \uparrow^6 10000\)
gulgolhexitoll E10,000#10,000#10,000#10,000#10,000#10,000#2 \(10 \uparrow^6 (10 \uparrow^6 10000)\)
gulgolduhexitoll E10,000#10,000#10,000#10,000#10,000#10,000#3 \(10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^6 10000))\)
gulgolgong E100,000#100,000#100,000#100,000#100,000#100,000 \(10 \uparrow^6 10^5\)
gulgolhexigong E100,000#100,000#100,000#100,000#100,000#100,000#2 \(10 \uparrow^6 (10 \uparrow^6 10^5)\)
gulgolduhexigong E100,000#100,000#100,000#100,000#100,000#100,000#3 \(10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^6 10^5))\)
gulgolbong E100,000,000#100,000,000#100,000,000#

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

\(10 \uparrow^6 10^8\)
gulgolhexibong E100,000,000#100,000,000#100,000,000#

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

\(10 \uparrow^6 (10 \uparrow^6 10^8)\)
gulgolduhexibong E100,000,000#100,000,000#100,000,000#

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

\(10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^6 10^8))\)
gulgolthrong E100,000,000,000#100,000,000,000#100,000,000,000#

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

\(10 \uparrow^6 10^{11}\)
gulgolhexithrong E100,000,000,000#100,000,000,000#100,000,000,000#

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

\(10 \uparrow^6 (10 \uparrow^6 10^{11})\)
gulgolduhexithrong E100,000,000,000#100,000,000,000#100,000,000,000#

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

\(10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^6 10^{11}))\)
goggolchime E1#1#1#1#1#1000 \(10 \uparrow^6 1000\)
goggoltoll E1#1#1#1#1#10,000 \(10 \uparrow^6 10000\)
goggolgong E1#1#1#1#1#100,000 \(10 \uparrow^6 10^5\)
goggolbong E1#1#1#1#1#100,000,000 \(10 \uparrow^6 10^8\)
goggolthrong E1#1#1#1#1#100,000,000,000 \(10 \uparrow^6 10^{11}\)
googolhex E100#1#1#1#1#1#2 \(10 \uparrow^6 10^{100}\)
grangolhex E100#100#1#1#1#1#2 \(10 \uparrow^6 (10 \uparrow^2 100)\)
greagolhex E100#100#100#1#1#1#2 \(10 \uparrow^6 (10 \uparrow^3 100)\)
gigangolhex E100#100#100#100#1#1#2 \(10 \uparrow^6 (10 \uparrow^4 100)\)
gulgolplex E(E100#100#100#100#100#100) \(10 \uparrow (10 \uparrow^6 100)\)
gulgoldex E100#(E100#100#100#100#100#100) \(10 \uparrow^2 (10 \uparrow^6 100)\)
gulgolthrex E100#100#(E100#100#100#100#100#100) \(10 \uparrow^3 (10 \uparrow^6 100)\)
gulgoltetrex E100#100#100#(E100#100#100#100#100#100) \(10 \uparrow^4 (10 \uparrow^6 100)\)
gulgolpentex E100#100#100#100#(E100#100#100#100#100#100)

= E100#100#100#100#100#101

\(10 \uparrow^5 (10 \uparrow^6 100)\)
ecetonhex E303#1#1#1#1#1#2 \(10 \uparrow^6 10^{303}\)
ecetonduhex E303#1#1#1#1#1#3 \(10 \uparrow^6 (10 \uparrow^6 10^{303})\)
ecetontrihex E303#1#1#1#1#1#4 \(10 \uparrow^6 (10 \uparrow^6 (10 \uparrow^6 10^{303}))\)
tria-octaxis E1#1#1#1#1#1#3 \(10 \uparrow^7 3\)
tetra-octaxis E1#1#1#1#1#1#4 \(10 \uparrow^7 4\)
deka-octaxis E1#1#1#1#1#1#10 \(10 \uparrow^7 10\)
hecta-octaxis E1#1#1#1#1#1#100 \(10 \uparrow^7 100\)
chilia-octaxis E1#1#1#1#1#1#1000 \(10 \uparrow^7 1000\)
myria-octaxis E1#1#1#1#1#1#10,000 \(10 \uparrow^7 10000\)

## Etymology

Parts of names Meaning
tria 3
tetra 4
penta 5
hexa 6
hepta 7
octa 8
enna 9
deka 10
hecta 100
chilia 1000
myria 10000
ding multiply the base value by 5
chime multiply the base value by 10
bell multiply the base value by 50
toll multiply the base value by 100
gong multiply the base value by 1000
bong multiply the base value by \(10^6\)
throng multiply the base value by \(10^9\)
gandingan multiply the base value by \(10^{12}\)

## Sources

1. Sbiis Saibian, 4.3.2 - Hyper-E Numbers