A051915 Numbers k such that 2*k! + 1 is prime.

0, 1, 2, 3, 5, 12, 18, 35, 51, 53, 78, 209, 396, 4166, 9091, 9587, 13357, 15917, 17652, 46127, 66480

Offset: 1

Author

Labos Elemer, Dec 18 1999

Keywords

• nonn
• more

Comments

Used PrimeForm to prove primality for n = 4166 (classical N-1 test). - David Radcliffe, May 28 2007

a(22) > 80000. - Serge Batalov, Jun 09 2025

Examples

			k = 5 is here because 2*5! + 1 = 241 is prime.
		

Crossrefs

Cf. A002981, A076679, A076680, A076681, A076682, A076683, A178488, A180626, A126896.

Programs

Magma

[n: n in [0..1000] | IsPrime(2*Factorial(n) +1)]; // Vincenzo Librandi, Feb 21 2015

Mathematica

Select[Range[0, 400], PrimeQ[2*#! + 1] &] (* Vladimir Joseph Stephan Orlovsky, Feb 13 2012 *)

PARI

is(k) = ispseudoprime(2*k!+1); \\ Jinyuan Wang, Feb 05 2020

Extensions

4166 from David Radcliffe, May 28 2007

More terms from Serge Batalov, Feb 18 2015

a(21) from Serge Batalov, Jun 08 2025