A139921 Primes of the form 3x^2+104y^2.

3, 107, 131, 179, 251, 347, 419, 443, 467, 491, 563, 659, 971, 1091, 1187, 1283, 1427, 1499, 1667, 1811, 1907, 1979, 2003, 2027, 2339, 2531, 2843, 2939, 2963, 3251, 3299, 3371, 3467, 3539, 3779, 3851, 3923, 4091, 4211, 4523, 4547, 4787

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1248. 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

[3] cat [ p: p in PrimesUpTo(6000) | p mod 312 in [35, 107, 131, 155, 179, 251]]; // Vincenzo Librandi, Aug 01 2012

Mathematica

QuadPrimes2[3, 0, 104, 10000] (* see A106856 *)

Formula

Except for 3, the primes are congruent to {35, 107, 131, 155, 179, 251} (mod 312).