A215714 Sophie Germain primes q such that q^2 + q + 41 is prime.

2, 3, 5, 11, 23, 29, 53, 83, 113, 131, 179, 191, 233, 281, 293, 359, 419, 509, 641, 653, 659, 683, 719, 743, 809, 911, 953, 1013, 1019, 1103, 1289, 1439, 1481, 1511, 1601, 1733, 1811, 1901, 1931, 2003, 2039, 2339, 2393, 2549, 2693, 2903, 2939, 3023, 3299, 3329

Offset: 1

Author

Pierre CAMI, Aug 21 2012

Keywords

• nonn

Comments

By definition, p = 2 * q + 1 is prime and (p^2 + 163)/4 = q^2 + q + 41 is also prime.

Examples

			29 is in the sequence because not only is 2 * 29 + 1 = 59 a prime, so is 29^2 + 29 + 41 = 911.
		

Links

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

Crossrefs

Cf. A005384, A005846.

Programs

Mathematica

Select[Prime[Range[500]], PrimeQ[2# + 1] && PrimeQ[#^2 + # + 41] &] (* Alonso del Arte, Aug 21 2012 *)

Formula

A005384 INTERSECT A056561. - R. J. Mathar, Aug 23 2012