A139855 Primes of the form 4x^2+4xy+31y^2.

31, 79, 151, 199, 271, 439, 631, 751, 919, 991, 1039, 1231, 1279, 1399, 1471, 1759, 1831, 1879, 1951, 1999, 2239, 2311, 2551, 2671, 2719, 2791, 3079, 3271, 3319, 3391, 3511, 3559, 3631, 3919, 4111, 4159, 4231, 4519, 4591, 4639, 4759, 4831

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant = -480. See A139827 for more information.

Also primes of the form 15x^2+16y^2, which has discriminant = -960. - T. D. Noe, May 07 2008

Also primes of the form 16x^2+8xy+31y^2, which has discriminant = -1920. See A140633. - T. D. Noe, May 19 2008

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
• William C. Jagy and Irving Kaplansky, Positive definite binary quadratic forms that represent the same primes [Cached copy] See item 14 in Table II.
• 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 {31, 79}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

QuadPrimes2[4, -4, 31, 10000] (* see A106856 *)

Formula

The primes are congruent to {31, 79} (mod 120).