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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 $$g_{\omega^{\omega^{\omega^26+\omega6+8}6}}(10)$$ $$g_{\omega^{\omega^{\omega^26+\omega6+8}7}}(10)$$

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