A139948 Primes of the form 19x^2+4xy+19y^2.

19, 103, 223, 271, 307, 523, 727, 859, 1039, 1063, 1123, 1279, 1291, 1447, 1483, 1531, 1543, 1699, 1783, 1879, 1951, 1987, 2287, 2371, 2467, 2551, 2707, 2719, 2803, 2971, 3079, 3163, 3307, 3331, 3391, 3583, 3727, 3919, 4003, 4231, 4339

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1428. See A139827 for more information.

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(6000) | p mod 1428 in [19, 55, 103, 115, 223, 271, 307, 355, 451, 475, 523, 535, 559, 727, 859, 871, 943, 1039, 1063, 1123, 1147, 1279, 1291, 1375]];// Vincenzo Librandi, Aug 02 2012

Mathematica

Union[QuadPrimes2[19, 4, 19, 10000], QuadPrimes2[19, -4, 19, 10000]] (* see A106856 *)

Formula

The primes are congruent to {19, 55, 103, 115, 223, 271, 307, 355, 451, 475, 523, 535, 559, 727, 859, 871, 943, 1039, 1063, 1123, 1147, 1279, 1291, 1375} (mod 1428).