A139656 Primes of the form x^2 + 312*y^2.

313, 337, 433, 601, 673, 937, 1153, 1249, 1297, 1609, 1777, 1873, 1993, 2089, 2161, 2473, 2521, 2617, 2713, 2833, 2857, 3121, 3169, 3433, 3457, 3769, 3793, 4057, 4177, 4273, 4657, 4729, 4801, 4969, 4993, 5113, 5209, 5281, 5521, 5641, 5737

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1248. See A139643 for more information.

The primes are congruent to {1, 25, 49, 121, 217, 289} (mod 312).

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)

Programs

Magma

[ p: p in PrimesUpTo(7000) | p mod 312 in {1, 25, 49, 121, 217, 289}]; // Vincenzo Librandi, Jul 29 2012

Magma

k:=312; [p: p in PrimesUpTo(6000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 312, 10000] (* see A106856 *)