Fermat primality test information

The Fermat primality test is a probabilistic test to determine whether a number is a probable prime. Fermat's little theorem states that if p is prime...

probably prime. The simplest probabilistic primality test is the Fermat primality test (actually a compositeness test). It works as follows: Given an integer...

successfully passes the Fermat primality test for the base a. The false statement that all numbers that pass the Fermat primality test for base 2 are prime is...

Fermat number Fermat point Fermat–Weber problem Fermat polygonal number theorem Fermat polynomial Fermat primality test Fermat pseudoprime Fermat quintic threefold...

{\displaystyle N} is prime. It produces a primality certificate to be found with less effort than the Lucas primality test, which requires the full factorization...

adopted a Fermat primality test as an alternative option for primality testing,[clarification needed] while keeping the Lucas-Lehmer test as a double-check...

Standard probabilistic primality tests such as the Baillie–PSW primality test, the Fermat primality test, and the Miller–Rabin primality test also produce compositeness...

be claimed and distributed by GIMPS. Prime95 tests numbers for primality using the Fermat primality test (referred to internally as PRP, or "probable...

In computational number theory, the Lucas test is a primality test for a natural number n; it requires that the prime factors of n − 1 be already known...

Baillie–PSW primality test Miller–Rabin primality test Lucas–Lehmer primality test Lucas–Lehmer test for Mersenne numbers AKS primality test Pollard's p − 1...

Fermat numbers' size, it is difficult to factorize or even to check primality. Pépin's test gives a necessary and sufficient condition for primality of...

strict converse of Fermat's Little Theorem does not hold. This fact precludes the use of that theorem as an absolute test of primality. The Carmichael numbers...

The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created...

is called primality. A simple but slow method of checking the primality of a given number n {\displaystyle n} , called trial division, tests whether n...

Primality Testing for Beginners is an undergraduate-level mathematics book on primality tests, methods for testing whether a given number is a prime number...

Wonderlic Test Ames test Chi-squared test Draize test Dixon's Q test F-test Fisher's exact test GRIM test Kolmogorov–Smirnov test Kuiper's test Likelihood-ratio...

curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods in primality proving...

test with a Fermat primality test, say, to base 2, one can obtain very powerful probabilistic tests for primality, such as the Baillie–PSW primality test...

deterministic primality tests, such as the AKS primality test, do not give false positives; there are no pseudoprimes with respect to them. Fermat's little theorem...

Miller–Rabin primality test. All prime numbers pass this test, but a small fraction of composites also pass, making them "pseudoprimes". Unlike the Fermat pseudoprimes...

quadratic sieve) and can be combined with the Fermat primality test to give the stronger Miller–Rabin primality test. The identity also holds in inner product...