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Prime factorization algorithm

A prime factorization algorithm is an algorithm (a step-by-step process) by which an integer (whole number) is "decomposed" into a product of factors that are prime numbers. The Fundamental Theorem of Arithmetic guarantees that this decomposition is unique.

Table of contents
1 A simple factorization algorithm
2 External link

A simple factorization algorithm


We can describe a recursive algorithm to perform such factorizations: given a number n

Note we need only primes p1 to p√n.

Time complexity

The described algoithm works fine for small n. However, for an 18-digit number (which has 60 digits in binary), all primes below about 1,000,000,000 may need to be tested, which is taxing even for a computer.

Adding two decimal digits to the original number will multiply the computation time by 10.

The difficulty (large time complexity) of factorization makes it a suitable basis for modern cryptography.

See also: Euler's Theorem, Integer factorization

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