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Primes p that have Kronecker symbol (p|14) = -1.
5

%I #24 Oct 23 2024 20:27:13

%S 11,17,29,31,37,41,43,47,53,67,73,89,97,103,107,109,149,163,167,179,

%T 197,199,211,223,241,257,271,277,311,313,317,331,347,353,367,373,379,

%U 383,389,409,421,433,439,443,479,491,499,503,521,541,547,557,571,577

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

%C Originally erroneously named "Primes that are not squares mod 14". - _M. F. Hasler_, Jan 18 2016

%C From _Jianing Song_, Nov 21 2019:

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

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

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

%H Vincenzo Librandi, <a href="/A191061/b191061.txt">Table of n, a(n) for n = 1..1000</a>

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

%o (Magma) [p: p in PrimesUpTo(577) | KroneckerSymbol(p, 14) eq -1]; // _Vincenzo Librandi_, Sep 11 2012

%Y Cf. A191017, A274504.

%K nonn,easy,changed

%O 1,1

%A _T. D. Noe_, May 25 2011

%E Definition corrected, following a suggestion from _David Broadhurst_, by _M. F. Hasler_, Jan 18 2016