A139883 Primes of the form 6x^2+6xy+31y^2.

31, 43, 67, 103, 151, 211, 283, 367, 463, 571, 691, 739, 751, 811, 823, 859, 919, 967, 991, 1123, 1171, 1279, 1291, 1399, 1447, 1459, 1471, 1483, 1531, 1567, 1627, 1663, 1699, 1783, 1831, 1867, 1879, 1987, 1999, 2083, 2179, 2239, 2311, 2371, 2383

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-708. 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(4000) | p mod 708 in {31, 43, 55, 67, 91, 103, 115, 151, 187, 211, 235, 247, 259, 283, 319, 367, 391, 415, 427, 451, 463, 511, 571, 583, 655, 667, 679, 691, 703}]; // Vincenzo Librandi, Jul 30 2012

Mathematica

QuadPrimes2[6, -6, 31, 10000] (* see A106856 *)

Formula

The primes are congruent to {31, 43, 55, 67, 91, 103, 115, 151, 187, 211, 235, 247, 259, 283, 319, 367, 391, 415, 427, 451, 463, 511, 571, 583, 655, 667, 679, 691, 703} (mod 708).