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A pseudoprime number is a probable prime number that might actually be a composite number rather than an actual prime. Pseudoprimes are useful in public key cryptography and other aspects of IT. IT professionals might talk about a pseudoprime as a number that may or may not be a true prime, but that could be brought up by random probable prime number generators.
The use of pseudoprime identifiers sometimes has to do with the cost of prime factoring for large numbers. Another use of the pseudoprime theory is in hacking philosophy. Here, an individual programmer might suggest that pseudoprimes are "almost as good" as true primes, because they stand a good chance of being actual primes, even though there is a chance that a single result might not be a true prime. Mathematicians can develop sophisticated algorithms to show whether a pseudoprime is actually a prime number or not.