A139867 Primes of the form 2x^2 + 2xy + 83y^2.

2, 83, 107, 167, 227, 263, 347, 503, 563, 743, 827, 887, 1163, 1187, 1223, 1283, 1427, 1487, 1583, 1667, 1823, 1847, 2063, 2087, 2207, 2243, 2543, 2903, 3167, 3203, 3407, 3467, 3527, 3803, 3863, 3923, 4127, 4463, 4523, 4583, 4703, 4787

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant = -660. 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(5000) | p mod 660 in {2, 83, 107, 167, 227, 263, 347, 503, 527, 563, 623}]; // Vincenzo Librandi, Jul 30 2012

Mathematica

QuadPrimes2[2, -2, 83, 10000] (* see A106856 *)

Formula

The primes are congruent to {2, 83, 107, 167, 227, 263, 347, 503, 527, 563, 623} (mod 660).