A139663 Primes of the form x^2 + 520*y^2.

521, 569, 601, 641, 809, 881, 1049, 1249, 1361, 1481, 1609, 1889, 2081, 2089, 2129, 2161, 2441, 2521, 2609, 2729, 3041, 3121, 3169, 3329, 3449, 3761, 3769, 3929, 4001, 4241, 4289, 4481, 4729, 4801, 4889, 4969, 5009, 5209, 5281, 5521, 5641

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant = -2080. See A139643 for more information.

The primes are congruent to {1, 9, 49, 81, 121, 129, 209, 289, 321, 329, 361, 441} (mod 520).

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 520 in {1, 9, 49, 81, 121, 129, 209, 289, 321, 329, 361, 441}]; // Vincenzo Librandi, Jul 29 2012

Magma

k:=520; [p: p in PrimesUpTo(6000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 520, 10000] (* see A106856 *)