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Let and
be Lucas Sequences generated by
and
, and define
A strong
Lucas pseudoprime is a Lucas Pseudoprime to the same base. Arnault (1997) showed that any Composite Number
is a strong Lucas pseudoprime for at most 4/15 of possible bases (unless
is the Product of Twin
Primes having certain properties).
See also Extra Strong Lucas Pseudoprime, Lucas Pseudoprime
References
Arnault, F. ``The Rabin-Monier Theorem for Lucas Pseudoprimes.'' Math. Comput. 66, 869-881, 1997.
Ribenboim, P. ``Euler-Lucas Pseudoprimes (elpsp(
)) and Strong Lucas Pseudoprimes (slpsp(
)).'' §2.X.C in
The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 130-131, 1996.