A139647 Primes of the form x^2 + 133*y^2.

137, 149, 197, 233, 277, 389, 457, 541, 557, 613, 617, 653, 701, 709, 757, 809, 821, 1033, 1061, 1201, 1213, 1289, 1297, 1373, 1429, 1453, 1493, 1597, 1621, 1733, 1873, 1901, 2053, 2069, 2129, 2137, 2153, 2213, 2221, 2297, 2381, 2417, 2437

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant=-532. See A139643 for more information.

The primes are congruent to {1, 9, 25, 81, 85, 93, 121, 137, 149, 169, 177, 197, 225, 233, 253, 277, 289, 305, 309, 365, 389, 429, 457, 473, 501, 505, 529} (mod 532).

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 532 in {1, 9, 25, 81, 85, 93, 121, 137, 149, 169, 177, 197, 225, 233, 253, 277, 289, 305, 309, 365, 389, 429, 457, 473, 501, 505, 529}]; // Vincenzo Librandi, Jul 28 2012

Magma

k:=133; [p: p in PrimesUpTo(3000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 133, 10000] (* see A106856 *)