High Quality Content by WIKIPEDIA articles! A pseudoprime is a probable prime (an integer which shares a property common to all prime numbers) which is not actually prime. Pseudoprimes can be classified according to which property they satisfy. The most important class of pseudoprimes come from Fermat's little theorem and hence are called Fermat pseudoprimes. This theorem states that if p is prime and a is coprime to p, then ap?1 ? 1 is divisible by p. If a number x is not prime, a > 1 is coprime to x and x divides ax?1 ? 1, then x is called a pseudoprime to base a. Some sources use variations of this definition, for example to only allow odd numbers to be pseudoprimes. A number x that is a pseudoprime for all values of a that are coprime to x is called a Carmichael number.

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