A139204 Numbers k such that (k!-9)/9 is prime.

6, 15, 17, 18, 21, 27, 29, 30, 37, 47, 50, 64, 125, 251, 602, 611, 1184, 1468, 5570, 10679, 15798, 21237

Offset: 1

Author

Artur Jasinski, Apr 11 2008

Keywords

• hard
• more
• nonn

Comments

a(20) > 10000. The PFGW program has been used to certify all the terms up to a(19), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, Mar 28 2014

a(23) > 25000. - Robert Price, Mar 29 2017

Crossrefs

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

Programs

Mathematica

a = {}; Do[If[PrimeQ[(n! - 9)/9], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a

PARI

for(n=1,1000,if(floor(n!/9-1)==n!/9-1,if(ispseudoprime(n!/9-1),print(n)))) \\ Derek Orr, Mar 28 2014

Extensions

a(14)-a(16) from Derek Orr, Mar 28 2014

a(17)-a(19) from Giovanni Resta, Mar 28 2014

a(20)-a(22) from Robert Price, Mar 29 2017