A139659 Primes of the form x^2 + 357*y^2.

373, 421, 457, 613, 757, 1033, 1381, 1429, 1453, 1549, 1597, 1789, 1801, 2053, 2269, 2293, 2389, 2473, 2797, 2857, 3061, 3109, 3217, 3229, 3313, 3469, 3613, 3637, 3697, 3889, 4201, 4657, 4813, 4909, 5653, 5737, 5881, 6073, 6133, 6337

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant = -1428. See A139643 for more information.

The primes are congruent to {1, 25, 121, 169, 205, 253, 361, 373, 421, 457, 529, 613, 625, 757, 781, 841, 865, 961, 1033, 1045, 1177, 1345, 1369, 1381} (mod 1428).

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 1428 in {1, 25, 121, 169, 205, 253, 361, 373, 421, 457, 529, 613, 625, 757, 781, 841, 865, 961, 1033, 1045, 1177, 1345, 1369, 1381}]; // Vincenzo Librandi, Jul 29 2012

Magma

k:=357; [p: p in PrimesUpTo(6400) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 357, 10000] (* see A106856 *)