A103319 Primes of the form p! + 1 where p is prime.

3, 7, 39916801, 13763753091226345046315979581580902400000001, 33452526613163807108170062053440751665152000000001, 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000001

Offset: 1

Author

Jonathan Sondow, Jan 31 2005

Keywords

• hard
• nonn

Comments

The values of p are 2, 3, 11, 37, 41, 73 which is A093804 (with a different definition). Subsequence of A088332 (primes of the form n! + 1).

Examples

			2 and 2! + 1 = 3 are prime, so 3 is a member.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, Section A2.

Links

• R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670, 2012 - From N. J. A. Sloane, Jun 13 2012
• Eric Weisstein's World of Mathematics, Factorial Prime
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A093804, A002981, A088332, A103318.

Programs

Mathematica

Select[Table[p!+1,{p,Prime[Range[30]]}],PrimeQ] (* Harvey P. Dale, Nov 28 2019 *)