A107190 Primes of the form 2x^2 + 39y^2.

2, 41, 47, 71, 89, 137, 167, 239, 281, 353, 359, 383, 401, 431, 449, 479, 593, 617, 743, 761, 839, 863, 929, 977, 983, 1097, 1103, 1151, 1217, 1289, 1319, 1367, 1409, 1487, 1553, 1601, 1607, 1697, 1721, 1913, 2039, 2087, 2111, 2153, 2273, 2351

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant=-312. See A107132 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)

Crossrefs

Cf. A139827.

Programs

Magma

[ p: p in PrimesUpTo(3000) | p mod 312 in {2, 41, 47, 71, 89, 119, 137, 161, 167, 215, 239, 281, 305} ]; // Vincenzo Librandi, Jul 28 2012

Mathematica

QuadPrimes2[2, 0, 39, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([2]), s=[41, 47, 71, 89, 119, 137, 161, 167, 215, 239, 281, 305]); forprime(p=41, lim, if(setsearch(s, p%312), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Formula

The primes are congruent to {2, 41, 47, 71, 89, 119, 137, 161, 167, 215, 239, 281, 305} (mod 312). - T. D. Noe, May 02 2008