login
Primes that are not squares mod 19.
4

%I #21 May 22 2022 09:49:40

%S 2,3,13,29,31,37,41,53,59,67,71,79,89,97,103,107,109,113,127,151,167,

%T 173,179,181,193,211,223,227,241,257,269,281,293,307,317,331,337,373,

%U 379,383,401,409,421,431,433,439,449,487,509,521,523,547,563,569,599

%N Primes that are not squares mod 19.

%C Inert rational primes in the field Q(sqrt(-19)). - _N. J. A. Sloane_, Dec 25 2017 [Corrected by _Jianing Song_, Dec 24 2018]

%C 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

%H Vincenzo Librandi, <a href="/A191063/b191063.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="https://oeis.org/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>

%t Select[Prime[Range[200]], JacobiSymbol[#,19]==-1&]

%o (Magma) [p: p in PrimesUpTo(599) | JacobiSymbol(p, 19) eq -1]; // _Vincenzo Librandi_, Sep 11 2012

%o (PARI) isok(p) = isprime(p) && !issquare(Mod(p, 19)); \\ _Michel Marcus_, Dec 25 2018

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 25 2011