The primitol is equal to s(3,2,2,2) in strong array notation.[1] It can be represented in chained arrow notation as \(3\rightarrow3\rightarrow2\rightarrow2\). In up arrow notation it is equal to \(3\uparrow\uparrow\cdots\uparrow\uparrow3\) with 27 arrows.


The name of this number is based on the word "primitive", meaning the top of primitive recursive arithmetic.


Notation Approximation
Up-arrow notation \(3\uparrow^{27}3\) (exact)
BEAF \(\{3,3,27\}\) (exact)
Hyper-E notation \(E2\#\#27\)
Chained arrow notation \(3\rightarrow3\rightarrow2\rightarrow2\) (exact)
Hyperfactorial array notation \(4!26\)
Fast-growing hierarchy \(f_{28}(2)\)
Hardy hierarchy \(H_{\omega^{28}}(2)\)
Slow-growing hierarchy \(g_{\varphi(26,0)}(3)\)


  1. Numbers from linear array notation | Steps Toward Infinity!

See alsoEdit

Hyp cos' linear strong array notation numbers | exAN numbers
3-entry series
Tribo group: tribo · tetbo · pentbo · hexabo
Trientri group: trientri · tettro · pentro · hextro
Trientet group: triteto · trientet · penteto · hexteto
Trienpent group: tripeno · tetpeno · trienpent · hexpeno
Trienhex group: trihexo · tethexo · penhexo · trienhex