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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Deterministic primality test for numbers of the form $A^2.3^n+1$, $n \ge 3$ odd


Authors: Pedro Berrizbeitia and Boris Iskra
Journal: Proc. Amer. Math. Soc. 130 (2002), 363-365
MSC (2000): Primary 11A51, 11Y11
Published electronically: September 19, 2001
MathSciNet review: 1862113
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Abstract: We use a result of E. Lehmer in cubic residuacity to find an algorithm to determine primality of numbers of the form $A^23^n+1$, $n$ odd, $A^2<4(3^n+1)$. The algorithm represents an improvement over the more general algorithm that determines primality of numbers of the form $A.3^n \pm 1$, $A/2<4.3^n-1$, presented by Berrizbeitia and Berry (1999).


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Additional Information

Pedro Berrizbeitia
Affiliation: Departamento de Matemáticas Puras y Aplicadas, Universidad Simón Bolívar, Caracas, Venezuela
Email: pedrob@usb.ve

Boris Iskra
Affiliation: Departamento de Matemáticas Puras y Aplicadas, Universidad Simón Bolívar, Caracas, Venezuela
Email: iskra@usb.ve

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06100-7
PII: S 0002-9939(01)06100-7
Received by editor(s): July 11, 2000
Published electronically: September 19, 2001
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2001 American Mathematical Society