Primitol

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Not to be confused with primitrol.

Primitol is equal to s(3,2,2,2) in strong array notation. 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.

Etymology

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

Approximations

Notation	Approximation
Arrow notation	\(3\uparrow^{27}3\) (exact)
Bowers' Exploding Array Function	\(\{3,3,27\}\) (exact)
Chained arrow notation	\(3\rightarrow3\rightarrow2\rightarrow2\) (exact)
Hyper-E notation	\(E3638334640023.7783\#7625597484984\#1\#2\#\#24\)
Hyperfactorial array notation	\(4!26\)
Fast-growing hierarchy	\(f_{28}(2)\)
Hardy hierarchy	\(H_{\omega^{28}}(2)\)
Slow-growing hierarchy	\(g_{\varphi(26,0)}(3)\)

See also

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

4-entry series

Primitol group: primitol · primitolplex · primitolbiplex · primitoltriplex · primitolquadriplex · primibol · primibolplex · primitrol · primitrolplex · primitetol · primitetolplex · primipenol · primipenolplex
Tetentri group: duprimitol · duprimitolplex · duprimibol · tetentri
Tetentet group: truprimitol · truprimitolplex · truprimibol · truprimibolplex · tetentet
Tetenpent group: quadprimitol · quadprimitolplex · quadprimibol · quadprimibolplex · tetenpent
Tetenhex group: quinprimitol · quinprimitolplex · quinprimibol · quinprimibolplex · tetenhex

5-entry series

Chainol group: chainol · chainolplex · chainolbiplex · chainoltriplex · chainolquadriplex · chainbol · chainbolplex · chaintrol · chaintrolplex
Chainprimol group: chainprimol · chainprimolplex · chainpribol · chainpribolplex · chainduprimol · chainduprimolplex · chaindupribol · chaindupribolplex · chaintruprimol · chaintruprimolplex · chaintrupribol · chaintrupribolplex
Pententri group: duchainol · duchainolplex · duchainbol · duchainbolplex · duchainprimol · duchainprimolplex · duchainpribol · duchainpribolplex · duchainduprimol · duchainduprimolplex · duchaindupribol · pententri
Pententet group: truchainol · truchainolplex · truchainbol · truchainbolplex · truchainprimol · truchainprimolplex · truchainpribol · truchainpribolplex · truchainduprimol · truchainduprimolplex · truchaindupribol · truchaindupribolplex · pententet · pentenpent · pentenhex

6-entry series

Choinol group: choinol · choinolplex · choinalbiplex · choinbol · choinbolplex · choinprimol · choinprimolplex · choinpribol · choinpribolplex · choinduprimol · choinduprimolplex · choindupribol · choindupribolplex
Choichainol group: choichainol · choichainolplex · choichainbolplex · choichainpribolplex · choichaindupribolplex · choiduchaindupribolplex
Hexentri group: hexentri · hexentet · hexenpent · hexenhex