A139923 Primes of the form 8x^2+39y^2.

47, 71, 167, 239, 359, 383, 431, 479, 743, 839, 863, 983, 1103, 1151, 1319, 1367, 1487, 1607, 2039, 2087, 2111, 2351, 2399, 2423, 2543, 2663, 2711, 2879, 2927, 3023, 3167, 3191, 3359, 3671, 3863, 3911, 4127, 4271, 4583, 4751, 4799, 4919

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-1248. See A139827 for more information.

Also primes of the form 15x^2+12xy+44y^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 312 in [47, 71, 119, 167, 215, 239]]; // Vincenzo Librandi, Aug 01 2012

Mathematica

QuadPrimes2[8, 0, 39, 10000] (* see A106856 *)

Formula

The primes are congruent to {47, 71, 119, 167, 215, 239} (mod 312).