A139652 Primes of the form x^2 + 232*y^2.

233, 241, 257, 281, 313, 353, 401, 457, 521, 593, 673, 761, 857, 929, 937, 953, 977, 1009, 1049, 1097, 1153, 1193, 1217, 1289, 1321, 1553, 1601, 1657, 1753, 1889, 1913, 2017, 2081, 2089, 2113, 2137, 2153, 2297, 2377, 2441, 2609, 2617, 2633

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant=-928. See A139643 for more information.

The primes are congruent to {1, 9, 25, 33, 49, 57, 65, 81, 121, 129, 161, 169, 209, 225} (mod 232).

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(3000) | p mod 232 in {1, 9, 25, 33, 49, 57, 65, 81, 121, 129, 161, 169, 209, 225}]; // Vincenzo Librandi, Jul 28 2012

Magma

k:=232; [p: p in PrimesUpTo(3000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 232, 10000] (* see A106856 *)