A107137 Primes of the form 2x^2 + 15y^2.

2, 17, 23, 47, 113, 137, 167, 233, 257, 263, 353, 383, 503, 593, 617, 647, 743, 857, 863, 887, 953, 977, 983, 1097, 1103, 1193, 1217, 1223, 1367, 1433, 1487, 1553, 1583, 1607, 1697, 1823, 1847, 1913, 2063, 2087, 2153, 2207, 2273, 2297, 2393

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -120. See A107132 for more information.

Links

• Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A139827.

Programs

Magma

[ p: p in PrimesUpTo(3000) | p mod 120 in {2, 17, 23, 47, 113} ]; // Vincenzo Librandi, Jul 24 2012

Mathematica

QuadPrimes2[2, 0, 15, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([2]), s=[17, 23, 47, 113]); forprime(p=11, lim, if(setsearch(s, p%120), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

The primes are congruent to {2, 17, 23, 47, 113} (mod 120). - T. D. Noe, May 02 2008