# Googology Wiki

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The googoli, coined with the googo- prefix, is equal to $$102^{51}$$ = g(2, 51, 102) in the Ackermann's Generalized Exponential Notation.[1][2] It is 103 digits long. Its full decimal representation is:

2,745,419,789,655,077,501,771,969,102,256,324,674,933,404,841,936,043,084,952,633,825,709,174,990,721,247,362,878,090,571,977,639,067,648

## Approximations

Notation Lower bound Upper bound
Scientific notation $$2.745\times10^{102}$$ $$2.746\times10^{102}$$
Arrow notation $$102\uparrow51$$
Steinhaus-Moser Notation 58[3] 59[3]
Copy notation 2[103] 3[103]
Taro's multivariable Ackermann function A(3,337) A(3,338)
Pound-Star Notation #*(13,3,9,5,4,5,2)*9 #*(0,4,9,5,4,5,2)*9
BEAF {102,51}
Hyper-E notation E[102]51
Hyperfactorial array notation 71! 72!
Fast-growing hierarchy $$f_2(331)$$ $$f_2(332)$$
Hardy hierarchy $$H_{\omega^2}(331)$$ $$H_{\omega^2}(332)$$
Slow-growing hierarchy $$g_{\omega^{51}}(102)$$