A pseudoprime is a composite number that passes certain tests for primality, making it appear to be a prime number. Specifically, it satisfies the conditions of the Fermat primality test, which checks if a number behaves like a prime under specific mathematical conditions. However, unlike true primes, pseudoprimes can be factored into smaller integers. The most well-known pseudoprimes are the Fermat pseudoprimes, which are composite numbers that remain undetected by the Fermat test for some bases. For example, the number 561 is a pseudoprime because it passes the test for several bases, even though it is not a prime number.