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

3, 7, 379, 6917, 208003

Offset

1,1

Comments

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

References

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

Links

Table of n, a(n) for n=1..5.

Eric Weisstein's World of Mathematics, Factorial Prime

Index entries for sequences related to factorial numbers.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A002982, A093804.

Sequence in context: A348376 A089689 A248701 * A104051 A128004 A281889

Adjacent sequences: A103314 A103315 A103316 * A103318 A103319 A103320

Keyword

nonn,hard,more

Author

Jonathan Sondow, Jan 31 2005

Extensions

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

Status

approved