A pseudoprime is a composite number that passes a test or sequence of tests that fail for most composite numbers. Unfortunately, some authors drop the "composite" requirement, calling any number that passes the specified tests a pseudoprime even if it is prime. Pomerance, Selfridge, and Wagstaff restrict their use of "pseudoprime" to odd composite numbers. "Pseudoprime" used without qualification means Fermat pseudoprime, i.e., a composite number that nonetheless satisfies Fermat's little theorem to some base or set of bases. Carmichael numbers are odd composite numbers that are Fermat pseudoprimes to every base; they are sometimes called absolute pseudoprimes.
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