Sequence of Prime Primorial minus 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:

$3, 5, 11, 13, 41, 89, 317, 337, 991, 1873, 2053, 2377, 4093, 4297, \ldots$

This sequence is A006794 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also see

• Definition:Primorial Prime

• Sequence of Prime Primorial plus 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): $29$

• 1987: H. Dubner: Factorial and primorial primes (J. Recr. Math. Vol. 19, no. 3: pp. 197 – 203)

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $29$