Multiplication method for factoring natural numbers

TL;DR

This paper introduces a multiplication-based factoring algorithm for large natural numbers with a runtime of O(n^{1/3}), extending Fermat's and Lehman's methods, and discusses its advantages, optimization potential, and finite algorithm validity.

Contribution

It presents a novel multiplication method for factoring that extends existing algorithms and analyzes its complexity and optimization possibilities.

Findings

Algorithm has O(n^{1/3}) complexity.

Comparative tests show advantages over related algorithms.

Optimization strategies can further reduce complexity.

Abstract

We offer multiplication method for factoring big natural numbers which extends the group of the Fermat's and Lehman's factorization algorithms and has run-time complexity $O(n^{1/3})$. This paper is argued the finiteness of proposed algorithm depending on the value of the factorizable number n. We provide here comparative tests results of related algorithms on a large amount of computational checks. We describe identified advantages of the proposed algorithm over others. The possibilities of algorithm optimization for reducing the complexity of factorization are also shown here.