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Pentafact is the mixed factorial of 5, written as 5*. The term was coined by SpongeTechX. It is equal to $$6,561 \uparrow\uparrow5$$ or 6,5616,5616,5616,5616,561.[1]

## Etymology

The name of this number is based on Greek prefix "penta-" and the word "factorial".

## Approximations in other notations

Notation Approximation
Scientific notation $$10^{10^{10^{5.273955688 \times 10^{25,043}}}}$$
Bird's array notation $$\{6561,5,2\}$$ (exact)
BEAF $$\{6561,5,2\}$$ (exact)
Graham Array Notation $$[6561,5,2]$$ (exact)
Strong Array Notation $$s(6561,5,2)$$ (exact)
Hyper-E notation $$E(6,561)6,561\#4$$ (exact)
Chained arrow notation $$6,561 \rightarrow 5 \rightarrow 2$$ (exact)
Hyperfactorial array notation $$9!1$$
Nested Factorial Notation $$9![2]$$
Fast-growing hierarchy $$f_3(5)$$
Hardy hierarchy $$H_{\omega^25}(6,561)$$
Slow-growing hierarchy $$g_{\omega^{\omega^{\omega^{\omega^{\omega}}}}}(6,561)$$ (exact)