Prime Factorization Algorithms

Many algorithms have been devised for determining the prime factors of a given number (a process called prime factorization). They vary quite a bit in sophistication and complexity. It is very difficult to build a general-purpose algorithm for this computationally "hard" problem, so any additional information that is known about the number in question or its factors can often be used to save a large amount of time.

The simplest method of finding factors is so-called "direct search factorization" (a.k.a. trial division). In this method, all possible factors are systematically tested using trial division to see if they actually divide the given number. It is practical only for very small numbers.

The fastest-known fully proven deterministic algorithm is the Pollard-Strassen method (Pomerance 1982; Hardy et al. 1990).

See also

Brent's Factorization Method, Class Group Factorization Method, Continued Fraction Factorization Algorithm, Direct Search Factorization, Dixon's Factorization Method, Elliptic Curve Factorization Method, Euler's Factorization Method, Excludent Factorization Method, Fermat's Factorization Method, Legendre's Factorization Method, Number Field Sieve, Pollard p-1 Factorization Method, Pollard rho Factorization Algorithm, Prime Factorization, Prime Number, Quadratic Sieve, Quiteprime, Trial Division, Veryprime, Williams p+1 Factorization Method Explore this topic in the MathWorld classroom

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Prime Factorization Algorithms

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