Gorgegol regiment

The gorgegol regiment is a series of numbers from E100#100#100#100#100 to E1#1#1#1#1#10,000 defined using Hyper-E Notation (i.e. beginning from gorgegol and up to myria-eptaxis).Sbiis Saibian, 4.3.2 - Hyper-E Numbers The numbers were coined by Sbiis Saibian.
Previous regiment	Next regiment
Gigangol regiment	Gulgol regiment
== List of numbers of the regiment ==
Name of number 	Hyper-E Notation (definition) 	Arrow notation (approximation) 	Fast-growing hierarchy (approximation)
Gorgegol 	E100#100#100#100#100 	\(10\uparrow^5 100\) 	\(f_6(100)\)
Gigangolpentex 	E100#100#100#100#1#2 	\(10\uparrow^5 (10\uparrow^4 100)\) 	\(f_6(f_5(100))\)
Gigangoltetrexipentex 	E100#100#100#100#2#2 	\(10\uparrow^5 (10\uparrow^4 (10\uparrow^4 100))\) 	\(f_6(f_5^2(100))\)
Gigangoldutetrexipentex 	E100#100#100#100#3#2 	\(10\uparrow^5 (10\uparrow^4 (10\uparrow^4 (10\uparrow^4 100)))\) 	\(f_6(f_5^3(100))\)
Gorgegolpentex 	E100#100#100#100#100#2 	\(10\uparrow^5 (10\uparrow^5 100)\) 	\(f_6^2(100)\)
Gigangoldupentex 	E100#100#100#100#1#3 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^4 100))\) 	\(f_6^2(f_5(100))\)
Gigangoltetrexidupentex 	E100#100#100#100#2#3 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^4 (10\uparrow^4 100)))\) 	\(f_6^2(f_5^2(100))\)
Gigangoldutetrexidupentex 	E100#100#100#100#3#3 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^4 (10\uparrow^4 (10\uparrow^4 100))))\) 	\(f_6^2(f_5^3(100))\)
Gorgegoldupentex 	E100#100#100#100#100#3 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 100))\) 	\(f_6^3(100)\)
Gigangoltripentex 	E100#100#100#100#1#4 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^4 100)))\) 	\(f_6^3(f_5(100))\)
Gigangoltetrexitripentex 	E100#100#100#100#2#4 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^4 (10\uparrow^4 100))))\) 	\(f_6^3(f_5^2(100))\)
Gigangoldutetrexitripentex	E100#100#100#100#3#4 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^4 (10\uparrow^4 (10\uparrow^4 100)))))\)	\(f_6^3(f_5^3(100))\)
Gorgegoltripentex 	E100#100#100#100#100#4 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^5 100)))\) 	\(f_6^4(100)\)
Gorgegolquadripentex 	E100#100#100#100#100#5 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^5 100))))\) 	\(f_6^5(100)\)
Gorgegolquintipentex 	E100#100#100#100#100#6 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^5 100)))))\)	\(f_6^6(100)\)
Gorgegolchime 	E1000#1000#1000#1000#1000 	\(10\uparrow^5 1000\) 	\(f_6(1000)\)
Gorgegolpentexichime 	E1000#1000#1000#1000#1000#2 	\(10\uparrow^5 (10\uparrow^5 1000)\) 	\(f_6^2(1000)\)
Gorgegoldupentexichime 	E1000#1000#1000#1000#1000#3 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 1000))\) 	\(f_6^3(1000)\)
Gorgegoltoll 	E10,000#10,000#10,000#10,000#10,000 	\(10\uparrow^5 10000\) 	\(f_6(10,000)\)
Gorgegolpentexitoll 	E10,000#10,000#10,000#10,000#10,000#2 	\(10\uparrow^5 (10\uparrow^5 10000)\) 	\(f_6^2(10,000)\)
Gorgegoldupentexitoll 	E10,000#10,000#10,000#10,000#10,000#3 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 10000))\) 	\(f_6^3(10,000)\)
Gorgegolgong 	E100,000#100,000#100,000#100,000#100,000 	\(10\uparrow^5 10^5\) 	\(f_6(100,000)\)
Gorgegolpentexigong 	E100,000#100,000#100,000#100,000#100,000#2	\(10\uparrow^5 (10\uparrow^5 10^5)\) 	\(f_6^2(100,000)\)
Gorgegoldupentexigong 	E100,000#100,000#100,000#100,000#100,000#3	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 10^5))\) 	\(f_6^3(100,000)\)
Gorgegolbong 	E100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000	\(10\uparrow^5 10^8\) 	\(f_6(10^8)\)
Gorgegolpentexibong 	E100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000#2	\(10\uparrow^5 (10\uparrow^5 10^8)\) 	\(f_6^2(10^8)\)
Gorgegoldupentexibong 	E100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000#3	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 10^8))\) 	\(f_6^3(10^8)\)
Gorgegolthrong 	E100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000	\(10\uparrow^5 10^{11}\) 	\(f_6(10^{11})\)
Gorgegolpentexithrong 	E100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000#2	\(10\uparrow^5 (10\uparrow^5 10^{11})\) 	\(f_6^2(10^{11})\)
Gorgegoldupentexithrong 	E100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000#3	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 10^{11}))\) 	\(f_6^3(10^{11})\)
Gigolchime 	E1#1#1#1#1000 	\(10\uparrow^5 1000\) 	\(f_6(1000)\)
Gigoltoll 	E1#1#1#1#10,000 	\(10\uparrow^5 10000\) 	\(f_6(10,000)\)
Gigolgong 	E1#1#1#1#100,000 	\(10\uparrow^5 10^5\) 	\(f_6(100,000)\)
Gigolbong 	E1#1#1#1#100,000,000 	\(10\uparrow^5 10^8\) 	\(f_6(10^8)\)
Gigolthrong 	E1#1#1#1#100,000,000,000 	\(10\uparrow^5 10^{11}\) 	\(f_6(10^{11})\)
Googolpentex 	E100#1#1#1#1#2 	\(10\uparrow^5 10^{100}\) 	\(f_6(f_2(323))\)
Grangolpentex 	E100#100#1#1#1#2 	\(10\uparrow^5 (10\uparrow^2 100)\) 	\(f_6(f_3(100))\)
Greagolpentex 	E100#100#100#1#1#2 	\(10\uparrow^5 (10\uparrow^3 100)\) 	\(f_6(f_4(100))\)
Gorgegolplex 	E(E100#100#100#100#100) 	\(10\uparrow (10\uparrow^5 100)\) 	\(f_2(f_6(100))\)
Gorgegoldex 	E100#(E100#100#100#100#100) 	\(10\uparrow^2 (10\uparrow^5 100)\) 	\(f_3(f_6(100))\)
Gorgegolthrex 	E100#100#(E100#100#100#100#100) 	\(10\uparrow^3 (10\uparrow^5 100)\) 	\(f_4(f_6(100))\)
Gorgegoltetrex 	E100#100#100#(E100#100#100#100#100) 	\(10\uparrow^4 (10\uparrow^5 100)\) 	\(f_5(f_6(100))\)
Ecetonpentex 	E303#1#1#1#1#2 	\(10\uparrow^5 10^{303}\) 	\(f_6(f_2(996))\)
Ecetondupentex 	E303#1#1#1#1#3 	\(10\uparrow^5 (10\uparrow^5 10^{303})\) 	\(f_6^2(f_2(996))\)
Ecetontripentex 	E303#1#1#1#1#4 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 10^{303}))\) 	\(f_6^3(f_2(996))\)
Ecetonquadripentex 	E303#1#1#1#1#5 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^5 10^{303})))\) 	\(f_6^4(f_2(996))\)
Ecetonquintipentex 	E303#1#1#1#1#6 	\(10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^5 (10\uparrow^5 10^{303}))))\) 	\(f_6^5(f_2(996))\)
Tria-eptaxis 	E1#1#1#1#1#3 	\(10\uparrow^6 3\) 	\(f_6^2(100)\)
Tetra-eptaxis 	E1#1#1#1#1#4 	\(10\uparrow^6 4\) 	\(f_6^3(100)\)
Deka-eptaxis 	E1#1#1#1#1#10 	\(10\uparrow^6 10\) 	\(f_7(9)\)
Hecta-eptaxis 	E1#1#1#1#1#100 	\(10\uparrow^6 100\) 	\(f_7(99)\)
Chilia-eptaxis 	E1#1#1#1#1#1000 	\(10\uparrow^6 1000\) 	\(f_7(999)\)
Myria-eptaxis 	E1#1#1#1#1#10,000 	\(10\uparrow^6 10000\) 	\(f_7(9999)\)
== 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 ==
Category:Saibian's regiments
Category:Numbers
Category:Numbers by Sbiis Saibian
Category:Series
Category:Up-arrow notation level