# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1903.12449