An absolute pseudoprime is a composite number that passes certain primality tests, making it appear prime. Specifically, it satisfies the conditions of the Fermat primality test for all bases less than the number itself. This means that when tested, it behaves like a prime number, even though it is not. These numbers are significant in number theory and cryptography because they can mislead algorithms that rely on primality testing. Understanding absolute pseudoprimes helps mathematicians improve the accuracy of these tests and develop more reliable methods for identifying true prime numbers, which are crucial for secure communications.