primtalstest

Primtalstest refers to any algorithm or method used to determine whether a given integer is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The simplest primality test is trial division, where one checks for divisibility by all integers from 2 up to the square root of the number being tested. If none of these numbers divide the target number evenly, it is prime. While effective for smaller numbers, trial division becomes computationally expensive for very large numbers.

More advanced primality tests exist, designed for greater efficiency. These include probabilistic tests like the Fermat primality test and the Miller-Rabin primality test. These tests do not guarantee primality but provide a high probability that a number is prime. If a number fails such a test, it is definitively composite. If it passes, it is considered a probable prime. For absolute certainty, deterministic primality tests are used, though they are generally more complex. The AKS primality test is a notable deterministic algorithm that runs in polynomial time, meaning its execution time grows polynomially with the size of the input number. The choice of primality test often depends on the size of the numbers involved and the required certainty of the result.