A139657 Primes of the form x^2 + 330*y^2.

331, 379, 499, 619, 691, 859, 1171, 1291, 1321, 1489, 1609, 1699, 2011, 2161, 2179, 2281, 2539, 2689, 2731, 2971, 3001, 3019, 3169, 3259, 3331, 3499, 3529, 3931, 4051, 4129, 4339, 4651, 4801, 5179, 5281, 5449, 5569, 5641, 5659, 5779, 6121

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1320. See A139643 for more information.

The primes are congruent to {1, 49, 91, 169, 289, 331, 361, 379, 499, 529, 619, 691, 841, 859, 889, 961, 1081, 1171, 1219, 1291} (mod 1320).

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 1320 in {1, 49, 91, 169, 289, 331, 361, 379, 499, 529, 619, 691, 841, 859, 889, 961, 1081, 1171, 1219, 1291}]; // Vincenzo Librandi, Jul 29 2012

Magma

k:=330; [p: p in PrimesUpTo(6200) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 330, 10000] (* see A106856 *)