Definition:Primorial/Positive Integer

Definition
Let $n$ be a positive integer.

Then:
 * $\ds n\# := \prod_{i \mathop = 1}^{\map \pi n} p_i = p_{\map \pi n}\#$

where $\map \pi n$ is the prime counting function.

That is, $n\#$ is defined as the product of all primes less than or equal to $n$.

Thus:
 * $n\# = \begin {cases}

1 & : n \le 1 \\ n \paren {\paren {n - 1}\#} & : \text {$n$ prime} \\ \paren {n - 1}\# & : \text {$n$ composite} \end {cases}$