A191063 Primes that are not squares mod 19.

2, 3, 13, 29, 31, 37, 41, 53, 59, 67, 71, 79, 89, 97, 103, 107, 109, 113, 127, 151, 167, 173, 179, 181, 193, 211, 223, 227, 241, 257, 269, 281, 293, 307, 317, 331, 337, 373, 379, 383, 401, 409, 421, 431, 433, 439, 449, 487, 509, 521, 523, 547, 563, 569, 599

Offset: 1

Author

T. D. Noe, May 25 2011

Keywords

• nonn
• easy

Comments

Inert rational primes in the field Q(sqrt(-19)). - N. J. A. Sloane, Dec 25 2017 [Corrected by Jianing Song, Dec 24 2018]

Primes p such that p^9 == -1 (mod 19). Primes congruent to {2, 3, 8, 10, 12, 13, 14, 15, 18} modulo 19. - Jianing Song, Dec 24 2018

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index to sequences related to decomposition of primes in quadratic fields

Programs

Magma

[p: p in PrimesUpTo(599) | JacobiSymbol(p, 19) eq -1]; // Vincenzo Librandi, Sep 11 2012

Mathematica

Select[Prime[Range[200]], JacobiSymbol[#,19]==-1&]
Select[Prime[Range[150]],PowerMod[#,9,19]==18&] (* Harvey P. Dale, Jun 29 2025 *)

PARI

isok(p) = isprime(p) && !issquare(Mod(p, 19)); \\ Michel Marcus, Dec 25 2018