论文信息 - Analysis of a Simple Factorization Algorithm

Analysis of a Simple Factorization Algorithm

Abstract The probability that the k th largest prime factor of a number n is at most n x is shown to approach a limit F k ( x ) as n → ∞. Several interesting properties of F k ( x ) are explored, and numerical tables are given. These results are applied to the analysis of an algorithm commonly used to find all prime factors of a given number. The average number of digits in the k th largest prime factor of a random m -digit number is shown to be asymptotically equivalent to the average length of the k th longest cycle in a permutation on m objects.

Donald E. Knuth | Luis Trabb Pardo | D. Knuth

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