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Gargoogolplex is a googolplex squared, or $$(10^{10^{100}})^2 = 10^{2\cdot10^{100}}.$$[1][2] 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 less than $$10^{10^{101}}$$. While gargoogolplex = $$(10^{10^{100}})^{2}$$, $$10^{10^{101}}$$ = $$(10^{10^{100}})^{10}$$.

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).

## Approximations

Notation Lower bound Upper bound
Arrow notation $$100\uparrow10\uparrow100$$
Down-arrow notation $$100\downarrow\downarrow51$$
Steinhaus-Moser Notation 56[3][3] 57[3][3]
Copy notation 1[1[101]] 2[2[101]]
Chained arrow notation $$100\rightarrow(10\rightarrow100)$$
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 {100,{10,100}}
Hyper-E notation 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 $$g_{\omega^{\omega^{\omega^2}2}}(10)$$