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Not to be confused with primitrol.

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.

## 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)
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 $$g_{\varphi(26,0)}(3)$$