A192579 Primes p for which there is no prime q == 3 (mod 4) that is smaller than p and is a quadratic residue modulo p.

2, 3, 5, 7, 17

Offset: 1

Author

Jonathan Sondow, Jul 04 2011

Keywords

• nonn
• fini
• full

Comments

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).

This is the unique set of primes answering the question in the Mathematics Stack Exchange link. - Rick L. Shepherd, May 29 2016

Examples

			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.
11 is not a member, because 3 < 11 and 3 == 5^2 (mod 11).
		

Links

• A. Gica, Quadratic residues of certain types, Rocky Mt. J. Math. 36 (2006), 1867-1871.
• A. Gica, Quadratic residues of certain types, Journées Arithmétiques 2011.
• Mathematics Stack Exchange, x, y, x - y and x + y are prime numbers. What is their sum?

Crossrefs

Cf. A192578.