A369863 Inert rational primes in the field Q(sqrt(-21)).

13, 29, 43, 47, 53, 59, 61, 67, 73, 79, 83, 97, 113, 127, 131, 137, 149, 151, 157, 163, 167, 181, 197, 211, 227, 229, 233, 241, 251, 281, 311, 313, 317, 331, 349, 379, 383, 389, 397, 401, 409, 419, 433, 449, 463, 467, 479, 487, 499, 503, 547, 557, 563, 569, 571, 577, 587

Offset: 1

Author

Dimitris Cardaris, Feb 03 2024

Keywords

• nonn

Comments

Primes p such that Legendre(-21,p) = -1.

Crossrefs

Cf. inert rational primes in the imaginary quadratic field Q(sqrt(-d)) for the first squarefree positive integers d: A002145 (1), A003628 (2), A003627 (3), A003626 (5), A191059 (6), A003625 (7), A296925 (10), A191060 (11), A105885 (13), A191061 (14), A191062 (15), A296930 (17), A191063 (19), this sequence (21), A191064 (22), A191065 (23).

Programs

Mathematica

Select[Range[3,600], PrimeQ[#] && JacobiSymbol[-21,#]==-1 &] (* Stefano Spezia, Feb 04 2024 *)

SageMath

[p for p in prime_range(3, 600) if legendre_symbol(-21, p) == -1]