Let be an Odd Integer, and assume there exists a Lucas Sequence with associated Sylvester Cyclotomic Numbers such that there is an (with and Relatively Prime) for which Divides . Then is a Prime unless it has one of the following two forms:
See also Lucas Sequence, Sylvester Cyclotomic Number
References
Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, pp. 69-70, 1989.