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Legion's number of the second kind is equal to \(666!^{666!} \approx 10^{1.609941\times10^{1,596}}\), where \(666!\) represents the factorial of 666.[1]

Approximations

Notation Lower bound Upper bound
Arrow notation \(770\uparrow338\uparrow631\) \(601\uparrow409\uparrow611\)
Down-arrow notation \(237\downarrow\downarrow673\) \(596\downarrow\downarrow576\)
Steinhaus-Moser Notation 576[3][3] 577[3][3]
Copy notation 1[1[1597]] 2[2[1597]]
H* function H(536H(530)) H(537H(530))
Taro's multivariable Ackermann function A(3,A(3,5301)) A(3,A(3,5302))
Pound-Star Notation #*((1))*((92))*17 #*((1))*((93))*17
BEAF {770,{338,631}} {601,{409,611}}
Hyper-E notation E[237]672#2 E[596]575#2
Bashicu matrix system (0)(1)[72] (0)(1)[73]
Hyperfactorial array notation (666!)! (667!)!
Fast-growing hierarchy \(f_2(f_2(5291))\) \(f_2(f_2(5292))\)
Hardy hierarchy \(H_{\omega^22}(5291)\) \(H_{\omega^22}(5292)\)
Slow-growing hierarchy \(g_{\omega^{\omega^{\omega^3+\omega^25+\omega9+6}}}(10)\) \(g_{\omega^{\omega^{\omega^3+\omega^25+\omega9+6}2}}(10)\)

See also

Sources

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