A139998 Primes of the form 31x^2+22xy+31y^2.

31, 199, 271, 439, 1039, 1231, 1279, 1399, 1879, 1951, 2239, 2551, 2719, 2791, 3079, 3391, 3559, 3631, 3919, 4231, 4591, 4639, 4759, 5431, 5479, 6079, 6151, 6271, 6991, 7159, 7591, 7759, 7951, 8431, 8599, 8839, 9439, 9511, 9631, 9679

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 31x^2+18xy+111y^2 and 31x^2+10xy+55y^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(12000) | p mod 840 in [31, 199, 271, 391, 439, 559]]; // Vincenzo Librandi, Aug 03 2012

Mathematica

Union[QuadPrimes2[31, 22, 31, 10000], QuadPrimes2[31, -22, 31, 10000]] (* see A106856 *)

Formula

The primes are congruent to {31, 199, 271, 391, 439, 559} (mod 840).