Primes not of form x^2 + 11*y^2.
2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 167, 173, 179, 181, 191, 193, 197, 211, 223, 227, 229, 233, 239, 241, 251, 263, 271, 277, 281, 283, 293, 307, 313, 317
1
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) k = 11; 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. A033209 (complement in the primes).
nonn
T. D. Noe, Jun 30 2014