Algorithm for determining whether a number is prime
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.
A primalitytest is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike...
The AKS primalitytest (also known as Agrawal–Kayal–Saxena primalitytest 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...
is the number of times we test a random a, and n is the value we want to test for primality; see Miller–Rabin primalitytest for details. There are infinitely...
{\displaystyle N} is prime. It produces a primality certificate to be found with less effort than the Lucas primalitytest, which requires the full factorization...
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...
curve primalitytesting techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods in primality proving...
test with a Fermat primalitytest, say, to base 2, one can obtain very powerful probabilistic tests for primality, such as the Baillie–PSW primality test...
Baillie–PSW primality test Miller–Rabin primalitytest Lucas–Lehmer primalitytest Lucas–Lehmer test for Mersenne numbers AKS primalitytest Pollard's p − 1...
F_{p\;-\,\left({\frac {5}{p}}\right)}.} The above formula can be used as a primalitytest in the sense that if n ∣ F n − ( 5 n ) , {\displaystyle n\mid F_{n\;-\...
relied primarily on the Lucas–Lehmer primalitytest as it is an algorithm that is both specialized for testing Mersenne primes and particularly efficient...
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 primalitytesting and integer factorization; these in turn are important in cryptography...
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...
be claimed and distributed by GIMPS. Prime95 tests numbers for primality using the Fermat primalitytest (referred to internally as PRP, or "probable...
computer scientist and mathematician noted for development of the AKS primalitytest, along with Manindra Agrawal and Nitin Saxena. Kayal was born and raised...
in the same interval is 1,091,987,404. Probable primality is a basis for efficient primalitytesting algorithms, which find application in cryptography...
PrimalityTesting for Beginners is an undergraduate-level mathematics book on primalitytests, methods for testing whether a given number is a prime number...
Pocklington primalitytest, while probable primes can be generated with probabilistic primalitytests such as the Baillie–PSW primalitytest or the Miller–Rabin...
hdl:21.11116/0000-0005-717D-0. Tao, Terence (2010). "1.11 The AKS primalitytest". An epsilon of room, II: Pages from year three of a mathematical blog...
executable test suite with the SUT. A test suite for a primalitytesting subroutine might consist of a list of numbers and their primality (prime or composite)...
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