A076133 Numbers k such that 2*k! - 1 is prime.

2, 3, 4, 5, 6, 7, 14, 15, 17, 22, 28, 91, 253, 257, 298, 659, 832, 866, 1849, 2495, 2716, 2773, 2831, 3364, 5264, 7429, 28539, 32123, 37868, 65591, 113920

Offset: 1

Author

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 30 2002

Keywords

• nonn
• more

Comments

a(32) > 116000. - Serge Batalov, Jun 06 2025

Examples

			k = 5 is here because 2*5! - 1 = 239 is prime.
		

Crossrefs

Cf. A051915.

Cf. A002982, A076134, A099350, A099351, A180627, A180628, A180629, A180630, A180631.

Programs

Magma

[n: n in [1..600] | IsPrime(2*Factorial(n)-1)]; // Vincenzo Librandi, Feb 20 2015

Mathematica

Select[Range[8000], PrimeQ[2 #! - 1] &] (* Vincenzo Librandi, Feb 20 2015 *)

PARI

is(k) = ispseudoprime(2*k!-1); \\ Jinyuan Wang, Feb 04 2020

Extensions

a(24)-a(29) from Serge Batalov, Feb 18 2015

a(30) from Serge Batalov, Jun 03 2025

a(31) from Serge Batalov, Jun 06 2025