Primes not of form x^2 + 13*y^2.
2, 3, 5, 7, 11, 19, 23, 31, 37, 41, 43, 47, 59, 67, 71, 73, 79, 83, 89, 97, 103, 107, 109, 127, 131, 137, 139, 149, 151, 163, 167, 179, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 251, 263, 271, 281, 283, 293, 307, 311, 317, 331, 347, 349, 353, 359
1
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) k = 13; nn = 30; t = Select[Union[Flatten[Table[x^2 + k*y^2, {x, 0, nn}, {y, 0, nn/Sqrt[k]}]]], # <= nn^2 + 1 && PrimeQ[#] &]; Complement[Prime[Range[PrimePi[nn^2 + 1]]], t]
Cf. A033210 (compliment in the primes).
nonn
T. D. Noe, Jun 30 2014