A139990 Primes of the form 12*x^2+12*x*y+73*y^2.

73, 97, 313, 433, 577, 937, 1153, 1657, 1753, 1777, 1993, 2113, 2593, 2617, 2833, 2953, 3433, 3457, 3673, 3793, 4177, 4273, 4297, 4513, 5113, 5857, 5953, 6793, 7297, 7537, 7873, 7993, 8377, 8713, 9337, 9817, 10177, 10513, 10657, 10993

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-3360. See A139827 for more information.

Also primes of the forms 48*x^2+24*x*y+73*y^2 and 33*x^2+12*x*y+52*y^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)

Programs

Magma

[p: p in PrimesUpTo(11000) | p mod 840 in [73, 97, 313, 433, 577, 817]]; // Vincenzo Librandi, Aug 03 2012

Mathematica

QuadPrimes2[12, -12, 73, 10000] (* see A106856 *)

Formula

The primes are congruent to {73, 97, 313, 433, 577, 817} (mod 840).