Jump to ContentJump to Main Navigation
Show Summary Details

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.

Export Citation

© 2012 by Walter de Gruyter Berlin Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Christian Aebi and Grant Cairns
The American Mathematical Monthly, 2015, Volume 122, Number 5, Page 433

Comments (0)

Please log in or register to comment.
Log in