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Analysis of a simple factorization algorithm

Authors
Journal
Theoretical Computer Science
0304-3975
Publisher
Elsevier
Publication Date
Volume
3
Issue
3
Identifiers
DOI: 10.1016/0304-3975(76)90050-5
Disciplines
  • Computer Science

Abstract

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.

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