A107210 Primes of the form 3x^2 + 31y^2.

3, 31, 43, 79, 127, 139, 151, 199, 223, 271, 331, 367, 463, 487, 499, 523, 571, 619, 631, 643, 739, 787, 823, 859, 883, 967, 991, 1171, 1231, 1447, 1483, 1531, 1543, 1567, 1579, 1627, 1747, 1759, 1951, 1987, 1999, 2011, 2083, 2131, 2287, 2311

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -372. 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(4000) | p mod 372 in {3, 31, 43, 55, 79, 91, 115, 127, 139, 151, 199, 223, 247, 259, 271, 331, 367}]; // Vincenzo Librandi, Jul 28 2012

Mathematica

QuadPrimes2[3, 0, 31, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([3]), s=[31, 43, 55, 79, 91, 115, 127, 139, 151, 199, 223, 247, 259, 271, 331, 367]); forprime(p=2, lim, if(setsearch(s, p%372), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Formula

The primes are congruent to {3, 31, 43, 55, 79, 91, 115, 127, 139, 151, 199, 223, 247, 259, 271, 331, 367} (mod 372). - T. D. Noe, May 02 2008