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...

number is likely to be prime, similar to the Fermat primality test and the Solovay–Strassen primality test. It is of historical significance in the search...

and 64 − 1 = 63 = 7 × 9 is a multiple of 7. Fermat's little theorem is the basis for the Fermat primality test and is one of the fundamental results of elementary...

The Solovay–Strassen primality test, developed by Robert M. Solovay and Volker Strassen in 1977, is a probabilistic primality test to determine if a number...

GIMPS adopted a Fermat primality test with basis a=3as an alternative option for primality testing, while keeping the Lucas-Lehmer test as a double-check...

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...

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

primality test? (more unsolved problems in mathematics) The Baillie–PSW primality test is a probabilistic or possibly deterministic primality testing...

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

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

Pépin's test is a primality test, which can be used to determine whether a Fermat number is prime. It is a variant of Proth's test. The test is named...

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...

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...

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

{\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...

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...

In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers. The test was originally developed by Édouard Lucas in 1878 and subsequently...

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...

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...

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

instead of primes. On the other hand, deterministic primality tests, such as the AKS primality test, do not give false positives; because of this, there...

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

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...

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

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...

due to a server error. First detected as a probable prime using Fermat primality test on an Nvidia A100 GPU on October 11, 2024 Stillwell, John (2010)...

primality. This all suggests a combined factoring method. Choose some bound a m a x > N {\displaystyle a_{\mathrm {max} }>{\sqrt {N}}} ; use Fermat's...

the Miller–Rabin primality test), 1.5 times that of a Lucas pseudoprimality test, and slightly more than a Baillie–PSW primality test. Note that the quadratic...