A191061 Primes p that have Kronecker symbol (p|14) = -1.

11, 17, 29, 31, 37, 41, 43, 47, 53, 67, 73, 89, 97, 103, 107, 109, 149, 163, 167, 179, 197, 199, 211, 223, 241, 257, 271, 277, 311, 313, 317, 331, 347, 353, 367, 373, 379, 383, 389, 409, 421, 433, 439, 443, 479, 491, 499, 503, 521, 541, 547, 557, 571, 577

Offset: 1

Author

T. D. Noe, May 25 2011

Keywords

• nonn
• easy

Comments

Originally erroneously named "Primes that are not squares mod 14". - M. F. Hasler, Jan 18 2016

From Jianing Song, Nov 21 2019: (Start)

Primes congruent to {11, 17, 29, 31, 33, 37, 41, 43, 47, 51, 53, 55} mod 56.

Rational primes that are remain inert in the field Q(sqrt(-14)). (End)

Primes p such that the Legendre symbol (-14/p) = -1, i.e., -14 is not a square modulo p. - Jianing Song, Oct 23 2024

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A191017, A274504.

Programs

Magma

[p: p in PrimesUpTo(577) | KroneckerSymbol(p, 14) eq -1]; // Vincenzo Librandi, Sep 11 2012

Mathematica

Select[Prime[Range[200]], JacobiSymbol[#,14]==-1&]

Extensions

Definition corrected, following a suggestion from David Broadhurst, by M. F. Hasler, Jan 18 2016