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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]

EtymologyEdit

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

Approximations in other notationsEdit

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)
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)

SourcesEdit

  1. SpongeTechX's Googology World

See alsoEdit

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