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%I #10 May 29 2016 17:36:55
%S 2,3,5,7,17
%N Primes p for which there is no prime q == 3 (mod 4) that is smaller than p and is a quadratic residue modulo p.
%C Gica proved that if p is a prime different from 2, 3, 5, 7, 17, then there exists a prime q < p which is a quadratic residue modulo p and q == 3 (mod 4).
%C This is the unique set of primes answering the question in the Mathematics Stack Exchange link. - _Rick L. Shepherd_, May 29 2016
%H A. Gica, <a href="http://dx.doi.org/10.1216/rmjm/1181069349">Quadratic residues of certain types</a>, Rocky Mt. J. Math. 36 (2006), 1867-1871.
%H A. Gica, <a href="http://atlas-conferences.com/cgi-bin/abstract/cbcw-66">Quadratic residues of certain types</a>, Journées Arithmétiques 2011.
%H Mathematics Stack Exchange, <a href="http://math.stackexchange.com/questions/250584/x-y-xy-and-x-y-are-prime-numbers-what-is-their-sum">x, y, x - y and x + y are prime numbers. What is their sum?</a>
%e p = 17 is a member, because the primes q < p with q == 3 (mod 4) are q = 3, 7, 11, and they are not quadratic residues modulo 17.
%e 11 is not a member, because 3 < 11 and 3 == 5^2 (mod 11).
%Y Cf. A192578.
%K nonn,fini,full
%O 1,1
%A _Jonathan Sondow_, Jul 04 2011
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