A139844 Primes of the form 2x^2 + 2xy + 53y^2.

2, 53, 113, 137, 197, 233, 317, 557, 617, 653, 953, 977, 1373, 1493, 1733, 1877, 1913, 1997, 2153, 2213, 2237, 2297, 2333, 2417, 2633, 2657, 2753, 2837, 3137, 3257, 3413, 3557, 3593, 3677, 3833, 3917, 4013, 4253, 4337, 4397, 4517, 4673

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant = -420. 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(5000) | p mod 420 in {2, 53, 113, 137, 197, 233, 317}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

QuadPrimes2[2, -2, 53, 10000] (* see A106856 *)

Formula

The primes are congruent to {2, 53, 113, 137, 197, 233, 317} (mod 420).