A139664 Primes of the form x^2 + 760*y^2.

761, 769, 809, 881, 929, 1049, 1201, 1289, 1489, 1601, 1721, 2129, 2281, 2441, 2609, 2969, 3041, 3049, 3089, 3121, 3209, 3329, 3361, 3769, 3881, 4001, 4129, 4241, 4409, 4481, 4561, 4721, 4729, 4889, 5441, 5521, 5641, 5801, 5849, 6089

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant = -3040. See A139643 for more information.

The primes are congruent to {1, 9, 49, 81, 121, 161, 169, 201, 289, 321, 329, 441, 481, 529, 609, 681, 689, 729} (mod 760).

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 760 in {1, 9, 49, 81, 121, 161, 169, 201, 289, 321, 329, 441, 481, 529, 609, 681, 689, 729}]; // Vincenzo Librandi, Jul 29 2012

Magma

k:=760; [p: p in PrimesUpTo(6100) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 760, 10000] (* see A106856 *)