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
(1980) restrict their use of "pseudoprime" to oddcomposite numbers.
Carmichael numbers are oddcomposite numbers that are Fermat pseudoprimes to
every base; they are sometimes called absolute pseudoprimes.
The following table gives the number of Poulet numbers psp(2), Euler-Jacobi pseudoprimes ejpsp(2),
and strong pseudoprimes spsp(2) to the base
2, and Carmichael numbers CN that are smaller
than the first few powers of 10 (Guy 1994). The table below extend Guy's table with
the results of Pinch, who calculated the number of pseudoprimes up to .