Note Integer Factoring Methods III

TL;DR

This paper introduces a new deterministic integer factorization algorithm with improved exponential time complexity of O(N^(1/6)), advancing the theoretical understanding of integer factoring methods.

Contribution

It presents a novel deterministic factorization algorithm with exponential time complexity O(N^(1/6)), improving upon previous methods.

Findings

New deterministic factorization algorithm with O(N^(1/6)) complexity

Algorithm for decomposing integers with specific factor difference form

Various theoretical results on integer decomposition

Abstract

The best deterministic unconditionally proven integer factorization algorithms have exponential running time complexities of O(N^(1/4)) arithmetic operations, and conditional on the Riemann hypothesis, there is a deterministic algorithm of exponential running time complexity O(N^(1/5)). This note proposes a new deterministic integer factorization algorithm of deterministic exponential time complexity O(N^(1/6)). Furthermore, an algorithm for decomposing composite integers that have factor differences of the form q - p = (r - 1)N^(1/2) + u, where r > 1 is a fixed parameter, and | u | < N^(1/3), in deterministic logarithmic time and various other results are included.