A139873 Primes of the form 13x^2 + 4xy + 13y^2.

13, 73, 193, 277, 337, 373, 457, 613, 673, 733, 853, 877, 937, 997, 1033, 1117, 1297, 1597, 1657, 1693, 1777, 1933, 1993, 2053, 2437, 2593, 2617, 2713, 2833, 2857, 2917, 3253, 3313, 3373, 3517, 3637, 3673, 4153, 4177, 4297, 4597, 4813, 4957

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant = -660. 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

[ p: p in PrimesUpTo(6000) | p mod 660 in {13, 73, 193, 217, 277, 337, 373, 457, 613, 637}]; // Vincenzo Librandi, Jul 30 2012

Mathematica

Union[QuadPrimes2[13, 4, 13, 10000], QuadPrimes2[13, -4, 13, 10000]] (* see A106856 *)

Formula

The primes are congruent to {13, 73, 193, 217, 277, 337, 373, 457, 613, 637} (mod 660).