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Pentafact is the mixed factorial of 5, written as 5*. The term was coined by SpongeTechX. It is equal to \(6561 \uparrow\uparrow5\) or 65616561656165616561.[1]

EtymologyEdit

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

Approximations in other notationsEdit

Notation Approximation
Bird's array notation \(\{6561,5,2\}\) (exactly equal)
BEAF \(\{6561,5,2\}\) (exactly equal)
Hyper-E notation \(E(6561)6561\#4\) (exactly equal)
Chained arrow notation \(6561 \rightarrow 5 \rightarrow 2\) (exactly equal)
Hyperfactorial array notation \(9!1\)
Nested Factorial Notation \(9![2]\)
Fast-growing hierarchy \(f_3(5)\)
Hardy hierarchy \(H_{\omega^25}(6561)\)
Slow-growing hierarchy \(g_{\omega^{\omega^{\omega^{\omega^{\omega}}}}}(6561)\) (exactly equal)

SourcesEdit

  1. SpongeTechX's Googology World

See alsoEdit

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