A139880 Primes of the form 13x^2+2xy+13y^2.

13, 61, 157, 181, 229, 349, 397, 661, 733, 829, 853, 997, 1021, 1069, 1237, 1669, 1693, 1741, 1861, 2029, 2341, 2677, 2749, 2917, 3037, 3181, 3253, 3373, 3517, 3541, 3709, 3853, 3877, 4021, 4093, 4261, 4357, 4549, 4597, 4861, 4933, 5101

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-672. See A139827 for more information.

Also primes of the forms 13x^2+4xy+52y^2 and 13x^2+8xy+40y^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 168 in {13, 61, 157}]; // Vincenzo Librandi, Jul 30 2012

Mathematica

Union[QuadPrimes2[13, 2, 13, 10000], QuadPrimes2[13, -2, 13, 10000]] (* see A106856 *)

Formula

The primes are congruent to {13, 61, 157} (mod 168).