The Leviathan number is equal to \(10^{666}! \approx 10^{6.6556570552\times10^{668}}\), where \(n!\) denotes the factorial.[1][2] It has \(2.5\times10^{665} - 143\) trailing zeros.

Approximations

Notation Lower bound Upper bound
Arrow notation \(284\uparrow312\uparrow268\) \(926\uparrow106\uparrow330\)
Down-arrow notation \(418\downarrow\downarrow256\) \(299\downarrow\downarrow271\)
Steinhaus-Moser Notation 273[3][3] 274[3][3]
Copy notation 5[5[669]] 6[6[669]]
H* function H(221H(221)) H(222H(221))
Taro's multivariable Ackermann function A(3,A(3,2220)) A(3,A(3,2221))
Pound-Star Notation #*((1))*((8))*12 #*((1))*((9))*12
BEAF {284,{312,268}} {926,{106,330}}
Hyper-E notation E[418]255#2 E[299]270#2
Bashicu matrix system (0)(1)[47] (0)(1)[48]
Hyperfactorial array notation (320!)! (321!)!
Fast-growing hierarchy \(f_2(f_2(2212))\) \(f_2(f_2(2213))\)
Hardy hierarchy \(H_{\omega^22}(2212)\) \(H_{\omega^22}(2213)\)
Slow-growing hierarchy \(g_{\omega^{\omega^{\omega^26+\omega6+8}6}}(10)\) \(g_{\omega^{\omega^{\omega^26+\omega6+8}7}}(10)\)

See also

Sources

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