Prime numbers and computer methods for factorization
Prime numbers and computer methods for factorization
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
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The theory of numbers is primarily concerned with the properties of the natural numbers 1,2,3,. . . . The fundamental theorem of arithmetic states that each natural number 1 can be expressed uniquely (up to order) as a product of prime numbers. A prime number is a natural number greater than 1 having no divisor other than 1 and itself. A natural number which is not prime is called composite. Proofs of the fundamental theorem provide no efficient method for obtaining the unique prime factorization of a natural number. The discovery of such methods is an important and difficult problem in number theory. This article will describe some algorithms for factoring integers, including the fastest ones known. It will be subdivided into these areas: