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 number | elliptic pseudoprime | Euler-Jacobi pseudoprime | Euler pseudoprime | extra strong Lucas pseudoprime | Fermat pseudoprime | Fibonacci pseudoprime | Frobenius pseudoprime | Lucas pseudoprime | Perrin pseudoprime | Poulet number | probable prime | Somer-Lucas pseudoprime | strong elliptic pseudoprime | strong Frobenius pseudoprime | strong Lucas pseudoprime | strong pseudoprime