Determination of the primality of by using factors of

Authors:
H. C. Williams and J. S. Judd

Journal:
Math. Comp. **30** (1976), 157-172

MSC:
Primary 10A25

MathSciNet review:
0396390

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Abstract: Algorithms are developed which can be used to determine the primality of a large integer *N* when a sufficient number of prime factors of are known. A test for the primality of *N* which makes use of known factors of and and the factor bounds on these numbers is also presented. In order to develop the necessary theory, the properties of some functions which are a generalization of Lehmer functions are used. Several examples of numbers proved prime by employing these tests are given.

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1976-0396390-3

Keywords:
Primality testing,
Lucas functions,
Lehmer functions

Article copyright:
© Copyright 1976
American Mathematical Society