Sequence of Prime Primorial plus 1

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 $\sequence p$ 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

• Sequence of Prime Primorial minus 1

Sources

• Apr. 1982: J.P. Buhler, R.E. Crandall and M.A. Penk: Primes of the Form $n! \pm 1$ and $2 \cdot 3 \cdot 5 \cdots p \pm 1$ (Math. Comp. Vol. 38, no. 158: pp. 639 – 643)  www.jstor.org/stable/2007298

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $31$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $31$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $24,029 \# + 1$