Generalized Lucas-Lehmer tests using Pell conics

Hambleton, Samuel

doi:10.1090/S0002-9939-2011-11196-1

Generalized Lucas-Lehmer tests using Pell conics
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by Samuel A. Hambleton

Proc. Amer. Math. Soc. 140 (2012), 2653-2661

DOI: https://doi.org/10.1090/S0002-9939-2011-11196-1

Published electronically: December 20, 2011

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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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