A139831 Primes of the form 2x^2+2xy+23y^2.

2, 23, 47, 83, 107, 167, 227, 263, 347, 383, 443, 467, 503, 563, 587, 647, 683, 743, 827, 863, 887, 947, 983, 1103, 1163, 1187, 1223, 1283, 1307, 1367, 1427, 1487, 1523, 1583, 1607, 1667, 1787, 1823, 1847, 1907, 2003, 2027, 2063, 2087, 2207

Offset

1,1

Comments

Discriminant=-180. See A139827 for more information.

Except for 2, also primes of the forms 3x^2+20y^2 (A107169) and 8x^2+4xy+23y^2. See A140633. - T. D. Noe, May 19 2008

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)

Formula

Except for 2, the primes are congruent to {23, 47} (mod 60).

Mathematica

QuadPrimes2[2, -2, 23, 10000] (* see A106856 *)

Prog

(Magma) [2] cat[ p: p in PrimesUpTo(3000) | p mod 60 in {23, 47}]; // Vincenzo Librandi, Jul 29 2012

Crossrefs

Sequence in context: A002428 A325145 A105440 * A049592 A054679 A057621

Adjacent sequences: A139828 A139829 A139830 * A139832 A139833 A139834

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved