Search results
Results from the WOW.Com Content Network
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.
In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently. These are used in various applications, for example hashing, public-key cryptography, and search of prime factors in large numbers. For relatively small numbers, it is possible to just apply trial division to each successive odd ...
In number theory, a provable prime is an integer that has been calculated to be prime using a primality-proving algorithm.Boot-strapping techniques using Pocklington primality test are the most common ways to generate provable primes for cryptography.
In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2 p + 1 associated with a Sophie Germain prime is called a safe prime . For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime.
For a long time, number theory in general, and the study of prime numbers in particular, was seen as the canonical example of pure mathematics, with no applications outside of mathematics [b] other than the use of prime numbered gear teeth to distribute wear evenly. [121]
Introduced by Jacobi in 1837, [1] it is of theoretical interest in modular arithmetic and other branches of number theory, but its main use is in computational number theory, especially primality testing and integer factorization; these in turn are important in cryptography.
An Euler probable prime to base a is an integer that is indicated prime by the somewhat stronger theorem that for any prime p, a (p−1)/2 equals () modulo p, where () is the Jacobi symbol. An Euler probable prime which is composite is called an Euler–Jacobi pseudoprime to base a. The smallest Euler-Jacobi pseudoprime to base 2 is 561.
The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, computer scientists at the Indian Institute of Technology Kanpur, on August 6, 2002, in an article titled "PRIMES is in P". [1]