Gargoogolplex

Gargoogolplex is a googolplex squared, or \((10^{10^{100}})^2 = 10^{2\cdot10^{100}}.\)A fuga really big numbersThe Fz, The Fuga & The Megafuga It was invented by Kieran Cockburn (Alistair's son), when he said "My space commander rules a gargoogolplex stars. It is a googolplex googolplexes." This number is the origin of the fuga- family of prefixes, introduced by his father, Alistair Cockburn, for the purpose of discussing how kids can make up more prefixes once they learn new mathematical vocabulary.
This number is less than both \(10^{10^{101}}\) and \(10^{100}!\); in terms of doubly exponential expressions they are very close. While \(10^{10^{101}} = (10^{10^{100}})^{10}\), gargoogolplex \(= (10^{10^{100}})^{2} = 10^{2 × 10^{100}} = 10^{10^{\log 2} × 10^{100}} = 10^{10^{100.301…}}\) .
Gargoogolplex should be interpreted as gar-googolplex, not gargoogol-plex. The latter equals to \(10^{10^{200}}\), which is a lot larger than a gargoogolplex (which has been named gargoogol-plexed). Sbiis Saibian has once mistakenly referred the googolplexian as gargoogolplex.[https://sites.google.com/site/pointlesslargenumberstuff/home/2/prefixesandsuffixes Saibian. Pointless Large Number Stuff (2).
==Approximations==
Notation 	Lower bound 	Upper bound
Arrow notation 	\(100\uparrow10\uparrow(100 + \log_{10}2) \approx 100\uparrow10\uparrow~100.301 \) (exact)	\(100\uparrow10\uparrow(100 + \log_{10}2) \approx 100\uparrow10\uparrow~100.301 \) (exact)
Down-arrow notation 	\(100\downarrow\downarrow51\) 	\(100\downarrow\downarrow51\)
Steinhaus-Moser Notation 	56[3][3] 	57[3][3]
Copy notation 	1[1[101]] 	2[2[101]]
Chained arrow notation 	\(100\rightarrow(10\rightarrow100)\) 	\(100\rightarrow(10\rightarrow100)\)
H* function 	H(6H(32)) 	H(7H(32))
Taro's multivariable Ackermann function	A(3,A(3,331)) 	A(3,A(3,332))
Pound-Star Notation 	#*((1))*(9,6,6,4,4)*7 	#*((1))*(0,7,6,4,4)*7
PlantStar's Debut Notation 	[1,59] 	[1,60]
BEAF & Bird's array notation 	{10,{10,~100.301}} (exact) 	{10,{10,~100.301}} (exact)
Hyper-E notation 	E[100]50#2 	E[100]50#2
Bashicu matrix system 	(0)(1)[18] 	(0)(1)[19]
Hyperfactorial array notation 	(69!)! 	(70!)!
Fast-growing hierarchy 	\(f_2(f_2(326))\) 	\(f_2(f_2(327))\)
Hardy hierarchy 	\(H_{\omega^22}(326)\) 	\(H_{\omega^22}(327)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega^{\omega^2}2}}(10)\) 	\(g_{\omega^{\omega^{\omega^2}2}}(10)\)
== Sources ==
== See also ==
ja:ガーグーゴルプレックス
zh:Gargoogolplex
Category:Numbers
Category:Numbers by Kieran Cockburn
Category:Numbers named by kids
Category:Numbers discussed by Alistair Cockburn
Category:Class 3
Category:Googol series
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