Sequence of Prime Primorial minus 1

Theorem
Let $p_n \#$ denote the $n$th primorial.

The sequence $\left\langle{n}\right\rangle$ such that $p_n \# - 1$ is prime begins:
 * $3, 5, 11, 13, 41, 89, 317, 337, 991, 1873, 2053, 2377, 4093, 4297, \ldots$