Ward's Primality Test

Let N be an odd integer, and assume there exists a Lucas sequence {U_n} with associated Sylvester cyclotomic numbers {Q_n} such that there is an n>sqrt(N) (with n and N relatively prime) for which N divides Q_n. Then N is a prime unless it has one of the following two forms:

1. N=(n-1)^2, with n-1 prime and n>4, or

2. N=n^2-1, with n-1 and n+1 prime.

See also

Lucas Sequence, Sylvester Cyclotomic Number

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Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 69-70, 1989.

Referenced on Wolfram|Alpha

Ward's Primality Test

Cite this as:

Weisstein, Eric W. "Ward's Primality Test." From MathWorld--A Wolfram Web Resource.

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