A140029 Primes of the form 3x^2+616y^2.

3, 619, 643, 691, 859, 1123, 1291, 1483, 1699, 2203, 2467, 2539, 2707, 2803, 2971, 3331, 3499, 3547, 4051, 4339, 4651, 4723, 4987, 5179, 5347, 5659, 6163, 6571, 6691, 7027, 7243, 7507, 8011, 8419, 8539, 9043, 9091, 9859, 9883, 9931, 10099

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

[3] cat [ p: p in PrimesUpTo(11000) | p mod 1848 in {115, 355, 619, 643, 691, 859, 955, 1027, 1123, 1147, 1291, 1483, 1651, 1699, 1819} ]; // Vincenzo Librandi, Aug 06 2012

Mathematica

QuadPrimes2[3, 0, 616, 10000] (* see A106856 *)

Formula

Except for 3, the primes are congruent to {115, 355, 619, 643, 691, 859, 955, 1027, 1123, 1147, 1291, 1483, 1651, 1699, 1819} (mod 1848).