A139859 Primes of the form 11x^2+2xy+11y^2.

11, 59, 131, 179, 251, 419, 491, 659, 971, 1019, 1091, 1259, 1451, 1499, 1571, 1619, 1811, 1931, 1979, 2099, 2339, 2411, 2459, 2531, 2579, 2699, 2819, 2939, 3011, 3251, 3299, 3371, 3491, 3539, 3659, 3779, 3851, 4019, 4091, 4139, 4211, 4259

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 11x^2+4xy+44y^2, 11x^2+10xy+35y^2 and 11x^2+8xy+56y^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 {11, 59}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

Union[QuadPrimes2[11, 2, 11, 10000], QuadPrimes2[11, -2, 11, 10000]] (* see A106856 *)

Formula

The primes are congruent to {11, 59} (mod 120).