# interpolating the primorials

Here’s a puzzle: consider that the Gamma function $\Gamma(z)$ is the interpolation of the factorials. What about interpolating the primorials. If $p_{n}$ is the \$n\$-th prime, then what is the correct analogue of the Gamma function if we define the primorial as:

$p_{n}\# = \prod_{k=1}^{n} p_{k}$