Definition:Primorial/Positive Integer

Definition
Let $n$ be a positive integer.

Then:
 * $\displaystyle n\# := \prod_{i \mathop = 1}^{\pi \left({n}\right)} p_i = p_{\pi \left({n}\right)}\#$

where $\pi \left({n}\right)$ 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 \left({\left({n - 1}\right)\#}\right) & : n \mbox { prime} \\ \left({n - 1}\right)\# & : n \mbox { composite} \end{cases}$