Sequence of Integers whose Factorial minus 1 is Prime

Sequence

The sequence of positive integers $n$ for which $n! - 1$ is prime begins:

$3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, 1963, 3507, 3610, 6917, 21 \, 480, 34 \, 790, 94 \, 550, 103 \, 040, 147 \, 855, 208 \, 003 \ldots$

This sequence is A002982 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

The sequence of corresponding primes begins:

$5, 23, 719, 5039, 479 \, 001 \, 599, 87 \, 178 \, 291 \, 199, \ldots$

This sequence is A055490 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also see

• Sequence of Integers whose Factorial plus 1 is Prime

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): $719$