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...

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

is the number of times we test a random a, and n is the value we want to test for primality; see Miller–Rabin primality test for details. There are infinitely...

The Miller–Rabin primality test or Rabin–Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number...

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...

algorithm lucas_primality_test is input: n > 2, an odd integer to be tested for primality. k, a parameter that determines the accuracy of the test. output: prime...

{\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...

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

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...

primality test? More unsolved problems in mathematics The Baillie–PSW primality test is a probabilistic or possibly deterministic primality testing algorithm...

multiple of 7. Fermat's little theorem is the basis for the Fermat primality test and is one of the fundamental results of elementary number theory. The...

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...

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

In computational number theory, the Adleman–Pomerance–Rumely primality test is an algorithm for determining whether a number is prime. Unlike other, more...

science, a primality certificate or primality proof is a succinct, formal proof that a number is prime. Primality certificates allow the primality of a number...

theory, but its main use is in computational number theory, especially primality testing and integer factorization; these in turn are important in cryptography...

Later Derrick Henry Lehmer refined Lucas's primality tests and obtained the Lucas–Lehmer primality test. He worked on the development of the umbral calculus...

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

their work on primality testing. In 1976 he was invited by Joseph Traub to meet at Carnegie Mellon University and presented the primality test, which Traub...

Pocklington's criterion can be used to prove the primality of 2p + 1 once one has proven the primality of p. Just as every term except the last one of...

in the same interval is 1,091,987,404. Probable primality is a basis for efficient primality testing algorithms, which find application in cryptography...

is a composite number that passes the Miller–Rabin primality test. All prime numbers pass this test, but a small fraction of composites also pass, making...

ACM Paris Kanellakis Award (with three others) for the Miller–Rabin primality test. He was made an ACM Fellow in 2002 and won the Knuth Prize in 2013....

relied primarily on the Lucas–Lehmer primality test as it is an algorithm that is both specialized for testing Mersenne primes and particularly efficient...

numbers is to generate random odd numbers and test them for primality. However, deterministic primality tests are slow. If the user is willing to tolerate...

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...

very weakly superpolynomial. For example, the Adleman–Pomerance–Rumely primality test runs for nO(log log n) time on n-bit inputs; this grows faster than...

algorithms include the Solovay–Strassen primality test, the Baillie–PSW primality test, the Miller–Rabin primality test, and certain fast variants of the Schreier–Sims...

Pocklington primality test, while probable primes can be generated with probabilistic primality tests such as the Baillie–PSW primality test or the Miller–Rabin...

Miller–Rabin primality test is guaranteed to run in polynomial time. (A polynomial-time primality test which does not require GRH, the AKS primality test, was...