A139667 Primes of the form x^2 + 1365*y^2.

1381, 1429, 1621, 2389, 2521, 3301, 4729, 5209, 5581, 5749, 5821, 6301, 6421, 6829, 6841, 7309, 7669, 8089, 8269, 8761, 8941, 9109, 9181, 9829, 9949, 10501, 10789, 11701, 12289, 12301, 12541, 12601, 13309, 13381, 13441, 13729, 14221

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant = -5460. See A139643 for more information.

The primes are congruent to {1, 121, 289, 361, 529, 589, 781, 841, 961, 1369, 1381, 1429, 1621, 1681, 1849, 2209, 2389, 2461, 2521, 2629, 2809, 2941, 3301, 3481, 3649, 3721, 3901, 3949, 4369, 4489, 4729, 4741, 5041, 5149, 5209, 5329} (mod 5460).

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

k:=1365; [p: p in PrimesUpTo(15000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 1365, 10000] (* see A106856 *)