MillerRabintyyppiset

MillerRabintyyppiset refers to a class of algorithms used for primality testing, specifically probabilistic tests. These algorithms are designed to determine whether a given number is likely prime or composite. Unlike deterministic primality tests, which provide a definitive answer, Miller-Rabin algorithms offer a high probability of correctness. They achieve this by employing a series of mathematical checks. If a number fails these checks, it is definitively composite. However, if it passes all the checks, it is considered a "strong probable prime" to the base used in the test. The probability of a composite number passing these tests for a single base is low, and this probability decreases exponentially as the number of bases tested increases. This makes Miller-Rabin a very efficient tool for primality testing in practice, especially for large numbers encountered in cryptography. The algorithm's efficiency stems from its reliance on number theoretic properties, specifically Fermat's Little Theorem and the properties of quadratic residues. While not guaranteeing absolute certainty, the confidence in the primality of a number after multiple Miller-Rabin tests can be made arbitrarily high, making it suitable for applications where absolute certainty is not strictly required or where computational cost is a significant factor.