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Macaulay2Doc :: isPseudoprime(ZZ)

isPseudoprime(ZZ) -- whether an integer is a pseudoprime

Synopsis

Description

The algorithm is provided by pari. The pseudoprimality test means that it has no small factors, that it is a Rabin-Miller pseudoprime for the base $2$, and that it passes the strong Lucas test for the sequence $(P, -1)$, where $P$ is the smallest positive integer such that $P^2 - 4$ is not a square modulo $x$. Such pseudoprimes may not be prime; to check primality, use isPrime. According to the documentation of pari, such pseudoprimes are known to be prime up to 1013, and no nonprime pseudoprime is known.