Some results on pseudosquares

Author:

Lukes R.,Patterson C.,Williams H.

Abstract

If p p is an odd prime, the pseudosquare L p L_p is defined to be the least positive nonsquare integer such that L p 1 ( mod 8 ) L_p\equiv 1\pmod {8} and the Legendre symbol ( L p / q ) = 1 (L_p/q)=1 for all odd primes q p q\le p . In this paper we first discuss the connection between pseudosquares and primality testing. We then describe a new numerical sieving device which was used to extend the table of known pseudosquares up to L 271 L_{271} . We also present several numerical results concerning the growth rate of the pseudosquares, results which so far confirm that L p > e p / 2 L_p> e^{\sqrt {p/2}} , an inequality that must hold under the extended Riemann Hypothesis.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference23 articles.

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