Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Generalized Lucas-Lehmer tests using Pell conics

Author: Samuel A. Hambleton
Journal: Proc. Amer. Math. Soc. 140 (2012), 2653-2661
MSC (2010): Primary 11Y11; Secondary 11G30
Published electronically: December 20, 2011
MathSciNet review: 2910753
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Abstract: Pell conics are used to write a Proth-Riesel twin-primality test. We discuss easy-to-find primality certificates for integers of the form $ m^n h \pm 1$. The known primality test for $ 3^n h \pm 1$ is associated with $ X^2+3Y^2 = 4$.

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Samuel A. Hambleton
Affiliation: School of Mathematics and Physics, University of Queensland, St. Lucia, Queensland, Australia 4072

Keywords: Pell conics, Lucas-Lehmer, primality
Received by editor(s): June 11, 2009
Received by editor(s) in revised form: November 9, 2010, and March 15, 2011
Published electronically: December 20, 2011
Communicated by: Ted Chinburg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.