Sequence of Integers whose Factorial plus 1 is Prime
(Redirected from Prime Numbers of form Factorial Plus 1)
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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
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): $1477! + 1$