A096292 Primes p such that p!-1 is divisible by the next prime larger than p.

3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607

Offset: 1

Author

Stuart Gascoigne (stuart.g(AT)scoigne.com), Jun 24 2004

Keywords

• nonn

Comments

This sequence includes A001359 as a subset, since the lesser of twin primes always satisfy this relation. The smallest number in this sequence that is not in A001359 is 7841. The only other known differences are 594278556271608991 and 4259842839142238791410741595983041626644087433.

Examples

			17 is here because 17!-1 is divisible by 19 and 19 is the next prime larger than 17.
		

Links

• Jeppe Stig Nielsen, Table of n, a(n) for n = 1..600
• Carlos Rivera, Puzzle 270.

Crossrefs

Cf. A001359, A286181.

Programs

PARI

p=2; forprime(q=3, , prod(j=1, p, Mod(j, q)) == 1 && print1(p, ", "); p=q) \\ Jeppe Stig Nielsen, Oct 04 2019