Asymmetric-key algorithms | Primality tests

Primality test

A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input). Some primality tests prove that a number is prime, while others like Miller–Rabin prove that a number is composite. Therefore, the latter might more accurately be called compositeness tests instead of primality tests. (Wikipedia).

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Lucas pseudoprime | Fibonacci number | Integer factorization | Randomized algorithm | Probable prime | AKS primality test | AC0 | Factorization | Lucas primality test | Deterministic algorithm | Agrawal's conjecture | Primitive root modulo n | RP (complexity) | Remainder | Strong pseudoprime | Fermat's little theorem | Big O notation | Adleman–Pomerance–Rumely primality test | Jacobi symbol | Proth's theorem | Greatest common divisor | Pseudoprime | The Art of Computer Programming | Trial division | Sieve of Eratosthenes | Sophie Germain prime | Miller–Rabin primality test | Co-NP | Cryptography | Primality certificate | Counterexample | Carmichael number | Primorial | John Selfridge | Generalized Riemann hypothesis | ZPP (complexity) | Composite number | Sample space | Baillie–PSW primality test | Multiplicative order | NC (complexity) | P-complete | L (complexity) | Mathematics | Pocklington primality test | Analytic number theory | R (programming language) | Wilson's theorem | Dart (programming language) | NP (complexity) | Prime number | Fermat primality test | Algorithm | Computational complexity theory | Frobenius pseudoprime | P (complexity) | Quasi-polynomial time | Euler pseudoprime | Modular arithmetic | Recursion | Shor's algorithm | Solovay–Strassen primality test