A102274 Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = -1, chi_{-7} = -1.

47, 59, 83, 131, 167, 227, 251, 311, 383, 419, 467, 479, 503, 563, 587, 647, 719, 839, 887, 971, 983, 1091, 1151, 1223, 1259, 1307, 1319, 1427, 1487, 1511, 1559, 1571, 1811, 1823, 1847, 1907, 1931, 1979, 2063, 2099, 2243, 2267, 2351, 2399, 2411, 2579, 2663, 2687, 2819, 2903, 2939, 2999

Offset: 1

Author

N. J. A. Sloane Feb 19 2005

Keywords

• nonn

Comments

Primes p such that p is 3 (mod 4) and (-3/p) = (-7/p) = -1, where (k/n) is the Kronecker symbol. - Robin Visser, Mar 13 2024

Links

• H. Cohn and J. C. Lagarias, On the existence of fields governing the 2-invariants of the classgroup of Q(sqrt{dp}) as p varies, Math. Comp. 41 (1983), 711-730.

Crossrefs

Cf. A102269, A102270, A102271, A102272, A102273, A102275.

Programs

Magma

[p : p in PrimesUpTo(3000) | p mod 84 in [47, 59, 83]];  // Robin Visser, Mar 13 2024

Formula

The primes are congruent to {47, 59, 83} (mod 84). - Robin Visser, Mar 13 2024

Extensions

More terms from Robin Visser, Mar 13 2024