Miller–Rabin primality test
The Miller–Rabin primality test is a probabilistic algorithm used to determine whether a given number is likely prime or composite. It is based on the properties of modular exponentiation and is widely used in cryptography and number theory due to its efficiency and reliability for large numbers. Unlike deterministic tests, it provides a high probability of correctness rather than absolute certainty, but with sufficient iterations, the error rate becomes negligible.
Developers should learn and use the Miller–Rabin test when working with cryptographic systems, such as RSA key generation, where fast primality testing is essential for security. It is particularly valuable for handling large integers where deterministic tests like trial division or the AKS primality test are too slow, offering a practical balance between speed and accuracy in applications like secure communication and digital signatures.