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Googoldubang or googolbangbang is equal to $$(10^{100}!)!$$.[1]

Aarex Tiaokhiao calls it googolbibang, facfacgol and googolbarxi.[2] It is also the tetorial of googol, or 10100!2 in Nested Factorial Notation.[3]

## Etymology

The name "googolbangbang" can be separated into 3 parts, "googol" and 2 "-bang"s, where the suffix "-bang" means factorial operation, so 2 "-bang"s means factorial operation applying 2 times.

## Approximations

Notation Lower bound Upper bound
Arrow notation $$10 \uparrow 10 \uparrow 10 \uparrow 101$$ $$10 \uparrow 10 \uparrow 10 \uparrow 102$$
Chained arrow notation $$10 \rightarrow (10 \rightarrow (10 \rightarrow 101))$$ $$10 \rightarrow (10 \rightarrow (10 \rightarrow 102))$$
Hyper-E notation $$E101\#3$$ $$E102\#3$$
Hyperfactorial array notation (10100!)!
H* function H(H(H(33)))) H(H(H(34))))
BEAF & Bird's array notation $$\{10,\{10,\{10,101\}\}\}$$ $$\{10,\{10,\{10,102\}\}\}$$
Fast-growing hierarchy $$f_2^{3}(332)$$ $$f_2^{3}(333)$$
Hardy hierarchy $$H_{\omega^23}(332)$$ $$H_{\omega^23}(333)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega^{\omega^2}+1}}}(10)$$ $$g_{\omega^{\omega^{\omega^{\omega^2}+2}}}(10)$$

## Sources

1. Aarex's large numbers (archived) (retrieved 2021-05-21)