A103317 Primes p such that p! - 1 is also prime.

3, 7, 379, 6917, 208003

Offset: 1

Author

Jonathan Sondow, Jan 31 2005

Keywords

• nonn
• hard
• more

Comments

The members are the primes in A002982 (n! - 1 is prime).

Examples

			3 is prime and 3! - 1 = 5 is prime, so 3 is a member.
		

References

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

Links

• Eric Weisstein's World of Mathematics, Factorial Prime
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A002982, A093804.

Programs

Mathematica

Select[Prime[Range[100]], PrimeQ[#! - 1] &] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2012 *)

PARI

isok(n) = ispseudoprime(n) && ispseudoprime(n!-1); \\ Jinyuan Wang, Jan 20 2020

Extensions

a(5)=208003 (found on Jul 27 2016, by Sou Fukui), added by Jinyuan Wang, Jan 20 2020