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This page is about Alistair Cockburn's definition. For the alternative definition, see Googolduplex.

The 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]]
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
BEAF {100,{10,100}}
Hyper-E notation E[100]50#2
Bashicu matrix system (0)(1)[330] (0)(1)[331]
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 \(g_{\omega^{\omega^{\omega^2}2}}(10)\)

Sources

  1. A fuga really big numbers
  2. The Fz, The Fuga & The Megafuga

See also

Numbers named with the fuga- family of prefixes

Gar-: garone · gartwo · garthree · garfour · garfive · garsix · garseven · gareight · garnine · garten · garhundred · gargoogol · gargoogolplex
Fz-: fzone · fztwo · fzthree · fzfour · fzfive · fzsix · fzseven · fzeight · fznine · fzten · fzeleven · fztwenty · fzhundred · fzgoogol · fzmillion · fzmilliplexion · fzgoogolplex · fzgargoogolplex · fzgargantugoogolplex
Fuga-: fugaone · fugatwo · fugathree · fugafour · fugafive · fugasix · fugaseven · fugaeight · fuganine · fugaten · fugahundred · fugagoogol · fugagoogolplex · fugagargoogolplex · fugagargantugoogolplex · fugagiggol
Megafuga-: megafugaone · megafugatwo · megafugathree · megafugafour · megafugafive · megafugasix · megafugaseven · megafugaeight · megafuganine · megafugaten · megafugaeleven · megafugatwelve · megafugathirteen · megafugafourteen · megafugafifteen · megafugasixteen · megafugaseventeen · megafugaeighteen · megafuganineteen · megafugatwenty · megafugathirty · megafugaforty · megafugafifty · megafugasixty · megafugaseventy · megafugaeighty · megafuganinety · megafugahundred · megafugagoogol · megafugagoogolplex · megafugagargoogolplex · megafugagargantugoogolplex
Booga-: boogaone · boogatwo · boogathree · boogafour · boogafive · boogasix · boogaseven · boogaeight · booganine · boogaten · boogahundred · boogagoogol · boogagoogolplex

Googol and related numbers