A140043 Primes of the form 47x^2+38xy+47y^2.

47, 311, 383, 647, 719, 839, 983, 1511, 2399, 2663, 2687, 3023, 3191, 3359, 4007, 4079, 4679, 4871, 5039, 5087, 5351, 5591, 5879, 5927, 6263, 6359, 6719, 7703, 7727, 8039, 8111, 8231, 8783, 9551, 9623, 9791, 9887, 10079, 10223, 10631, 11399

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-7392. 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(12000) | p mod 1848 in {47, 311, 335, 383, 551, 647, 719, 815, 839, 983, 1175, 1343, 1391, 1511, 1655} ]; // Vincenzo Librandi, Aug 06 2012

Mathematica

Union[QuadPrimes2[47, 38, 47, 10000], QuadPrimes2[47, -38, 47, 10000]] (* see A106856 *)

Formula

The primes are congruent to {47, 311, 335, 383, 551, 647, 719, 815, 839, 983, 1175, 1343, 1391, 1511, 1655} (mod 1848).