A139644 Primes of the form x^2 + 105*y^2.

109, 421, 541, 709, 1009, 1129, 1201, 1381, 1429, 1549, 1621, 1789, 1801, 2221, 2269, 2389, 2521, 2689, 3049, 3061, 3109, 3229, 3301, 3361, 3469, 3529, 3889, 4201, 4561, 4621, 4729, 4789, 4909, 5209, 5569, 5581, 5749, 5821, 5881, 6301

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant=-420. See A139643 for more information.

The primes are congruent to {1, 109, 121, 169, 289, 361} (mod 420).

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(7000) | p mod 420 in {1, 109, 121, 169, 289, 361}]; // Vincenzo Librandi, Jul 28 2012

Magma

k:=105; [p: p in PrimesUpTo(7000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 105, 10000] (* see A106856 *)