Fermat Primality Test
The Fermat Primality Test is a probabilistic algorithm used to determine if a number is likely prime, based on Fermat's Little Theorem. It checks whether a given integer n satisfies a^(n-1) ≡ 1 (mod n) for a random base a, where 1 < a < n-1. If the congruence fails for any a, n is definitely composite; if it holds, n is probably prime, but there are rare exceptions called Carmichael numbers.
Developers should learn this test when working in cryptography, number theory, or security applications that require prime number generation, such as RSA encryption or key exchange protocols. It's useful for quickly screening large numbers for primality with high probability, though it's not deterministic and should be supplemented with more rigorous tests like the Miller-Rabin test for critical applications.