A139860 Primes of the form 12x^2+12xy+13y^2.

13, 37, 157, 277, 373, 397, 613, 733, 757, 853, 877, 997, 1093, 1117, 1213, 1237, 1453, 1597, 1693, 1933, 2053, 2293, 2437, 2557, 2677, 2797, 2917, 3037, 3253, 3373, 3517, 3613, 3637, 3733, 3853, 3877, 4093, 4357, 4597, 4813, 4933, 4957

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-480. See A139827 for more information.

Also primes of the forms 13x^2+2xy+37y^2 and 13x^2+4xy+28y^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(6000) | p mod 120 in {13, 37}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

QuadPrimes2[12, -12, 13, 10000] (* see A106856 *)

Formula

The primes are congruent to {13, 37} (mod 120).

Extensions

Corrected and extended b-file - Ray Chandler, Jul 30 2014