A215697 Primes p = 2x + 1 such that x^2 + x + 41 is prime.

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 97, 101, 103, 107, 109, 127, 137, 139, 149, 151, 157, 167, 173, 181, 191, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 283, 293, 307, 313, 317, 331

Offset: 1

Author

Pierre CAMI, Aug 21 2012

Keywords

• nonn

Examples

			17 is in the sequence because, given x = (17 - 1)/2 = 8, we have 8^2 + 8 + 41 = 113 which is prime.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056561, A005846.

Programs

Mathematica

Select[Prime[Range[100]], PrimeQ[((# - 1)/2)^2 + ((# - 1)/2) + 41] &] (* Alonso del Arte, Aug 21 2012 *)

PARI

for(x=1, 1e3, if(ispseudoprime(2*x+1), if(ispseudoprime(x^2+x+41), print1(2*x+1, ", ")))) \\ Felix Fröhlich, Aug 16 2014