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Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem. To factorize a small integer n using mental or pen-and-paper arithmetic, the simplest method is trial division : checking if the number is divisible by prime numbers 2 ...
14.2 Integer factorization. 14.3 Pseudo-random numbers. 15 Arithmetic dynamics. 16 History. ... Cunningham project; Quadratic residuosity problem; Primality tests
In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial ...
The integer factorization problem is in NP and in co-NP (and even in UP and co-UP [23]). If the problem is NP-complete, the polynomial time hierarchy will collapse to its first level (i.e., NP = co-NP). The most efficient known algorithm for integer factorization is the general number field sieve, which takes expected time
Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special-purpose algorithm, meaning that it is only suitable for integers with specific types of factors; it is the simplest example of an algebraic-group factorisation algorithm.
Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. [ 1 ] It uses only a small amount of space, and its expected running time is proportional to the square root of the smallest prime factor of the composite number being factorized.
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