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A Property of Twin Primes

Christian Aebi / Grant Cairns
Published Online: 2012-08-01 | DOI: https://doi.org/10.1515/integers-2011-0121


We determine the product of the invertible quadratic residues in for odd n. This is a variation on Gauss' generalization of Wilson's theorem. From this we deduce that for twin primes , the product of the invertible quadratic residues in is , where the sign depends on the residue class of p modulo 4. We examine necessary and sufficient conditions for consecutive odd natural numbers to satisfy this property of twin primes. The paper concludes with two open questions.

Keywords: Twin Primes; Quadratic Residues; Wilson's Theorem

About the article

Received: 2011-02-08

Accepted: 2011-12-19

Published Online: 2012-08-01

Published in Print: 2012-08-01

Citation Information: Integers, Volume 12, Issue 4, Pages 521–527, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2011-0121.

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© 2012 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

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