Sequence of Integers whose Factorial plus 1 is Prime

Sequence

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

$0, 1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, 26 \, 951, 110 \, 059, 150 \, 209 \ldots$

This sequence is A002981 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

The sequence of corresponding primes begins:

$2, 2, 3, 7, 39 \, 916 \, 801, \ldots$

This sequence is A088332 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also see

• Sequence of Integers whose Factorial minus 1 is Prime

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $7$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $116$

• Apr. 1995: Chris K. Caldwell: On the Primality of $n! \pm 1$ and $2 \cdot 3 \cdot 5 \cdots p \pm 1$ (Math. Comp. Vol. 64, no. 210: pp. 889 – 890)  www.jstor.org/stable/2153458

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $7$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1477$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1477! + 1$