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Googolplexibit is equal to E[2]100#2 = 22100 ≈ 103.816×1029 using Hyper-E notation.[1] The name was coined by Sbiis Saibian. Saibian also denotes this number by "2^100#2", however this notation is never explicitly defined. It is 381,600,854,690,147,056,244,358,827,361 digits long.

Username5243 calls this number Binary-Googolplex, and it's equal to 2[1]2[1]100 in Username5243's Array Notation.[2]

Aarex Tiaokhiao calls this number binary-googolplex.[3]

The decimal expansion of googolplexibit is: 228,536,769,422,951,370,300,290,046,652,...,799,355,055,482,488,460,983,335,387,136.[4] The first digits can be computed by multiplying the base-10 logarithm of 2 by 2100, extracting the fractional part, and raising 10 to that power, while the last digits can be computed using modular exponentiation.

## Approximations

Notation Lower bound Upper bound
Arrow notation $$2\uparrow2\uparrow100$$
Down-arrow notation $$2\downarrow\downarrow101$$
Steinhaus-Moser Notation 21[3][3] 22[3][3]
Copy notation 3[3[30]] 4[4[30]]
H* function H(127H(8)) H(128H(8))
Taro's multivariable Ackermann function A(3,A(3,97)) A(3,A(3,98))
Pound-Star Notation #*((1))*(3,0,8)*4 #*((1))*(4,0,8)*4
BEAF {2,{2,100}}
Bashicu matrix system (0)(1)[9] (0)(1)[10]
Hyperfactorial array notation (27!)! (28!)!
Fast-growing hierarchy $$f_2(f_2(93))$$ $$f_2(f_2(94))$$
Hardy hierarchy $$H_{\omega^22}(93)$$ $$H_{\omega^22}(94)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega+8}4}}(16)$$

## Sources

1. Saibian, Sbiis. Hyper-E Numbers. Retrieved 2016-07-11.
2. Part 1 - My Large Numbers
3. Allam's Numbers - Googol and Googolplex. Retrieved 2021-06-17.

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