A090687 Primes of the form 6*k^2 + 1.

7, 97, 151, 487, 601, 727, 2647, 3457, 4057, 7351, 9127, 9601, 11617, 12697, 14407, 15607, 17497, 20887, 21601, 29401, 33751, 37447, 39367, 42337, 47527, 53017, 54151, 71287, 77977, 80737, 84967, 95257, 102967, 110977, 126151, 142297, 151687

Offset: 1

Author

Cino Hilliard, Dec 18 2003

Keywords

• easy
• nonn

Comments

Subset of A002476. See also A121326. The values of k for which 6*k^2 + 1 is prime are 1, 4, 5, 9, 10, 11, 21, 24, 26, 35, 39, 40, 44, 46, 49, 51, 54, 59, 60, 70, 75, 79, 81, 84, 89, 94, 95, 109, 114, 116, 119, 126, 131, 136, 145, 154, ... - Jonathan Vos Post, Aug 27 2006

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000040, A002476, A090686.

Programs

Magma

[a: n in [0..600] | IsPrime(a) where a is 6*n^2+1]; // Vincenzo Librandi, Dec 03 2011

Mathematica

Select[Table[6n^2+1,{n,0,1000}],PrimeQ] (* Vincenzo Librandi, Dec 03 2011 *)

PARI

mx2pmp(n) = { for(x=1,n, y = 6*x^2+1; if(isprime(y),print1(y",")) ) }

Extensions

Edited by N. J. A. Sloane at the suggestion of R. J. Mathar, Apr 14 2008