Deterministic Primality Tests
Deterministic primality tests are algorithms that, given an integer input, always correctly determine whether it is prime or composite, with no probability of error. These tests provide a definitive yes/no answer about primality, unlike probabilistic tests which have a small chance of false positives. They are fundamental in number theory and cryptography, where absolute certainty about primality is required.
Developers should learn deterministic primality tests when building cryptographic systems (e.g., RSA key generation), secure protocols, or mathematical applications that require guaranteed primality verification. They are essential in scenarios where even a tiny error probability is unacceptable, such as in generating large prime numbers for encryption keys or in rigorous mathematical proofs.