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Primality tests

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sieve of Eratosthenes
ancient algorithm for generating prime numbers
Wilson's theorem
necessary and sufficient condition for a number to be prime
primality test
algorithm for determining whether an input number is prime
Miller–Rabin primality test
probabilistic primality test
AKS primality test
primality test
Sieve of Atkin
primality test
Fermat primality test
primality test
Perrin number
Number sequence 3,0,2,3,2,5,5,7,10,... defined by recurrence relation P(n) = P(n-2) + P(n-3).
Lucas–Lehmer primality test
primality test
Lucas primality test
primality test
Solovay–Strassen primality test
probabilistic primality test
Sieve of Sundaram
algorithm for generating prime numbers
Proth's theorem
primality test for Proth numbers
Pépin's test
primality test for Fermat numbers
Prime95
Prime95, also distributed as the command-line utility mprime for FreeBSD, Linux, and MacOS is a freeware application written by George Woltman. It is the official client of the Great Internet Mersenne Prime Search (GIMPS), a volunteer computing project dedicated to searching for Mersenne primes. It is also used in overclocking to test for system stability.
Adleman–Pomerance–Rumely primality test
algorithm for determining whether a number is prime
Lucas–Lehmer–Riesel test
Test for determining whether a number is prime
Pocklington-Lehmer primality test
Number-theoretic algorithm
Baillie–PSW primality test
probabilistic primality testing algorithm
elliptic curve primality proving
methods to check primality
primality certificate
proof that a number is prime