Sequence of Prime Primorial plus 1

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Theorem

For prime $p$, let $p \#$ denote the $p$th primorial, defined in the sense that $p \#$ is the product of all primes less than or equal to $p$.

The sequence $\left\langle{p}\right\rangle$ such that $p \# + 1$ is prime begins:

$2, 3, 5, 7, 11, 31, 379, 1019, 1021, 2657, 3229, 4547, 4787, 11549, 13649, 18523, 23801, 24029, 42209, 145823, 366439, 392113, \ldots$

This sequence is A005234 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Also see


Sources