The use of the invariant's properties in the primality test and prime search

TL;DR

This paper explores invariant properties to develop new algorithms for primality testing and prime search, highlighting their advantages, disadvantages, and implications for factorization of composite numbers.

Contribution

It introduces novel algorithms based on invariant properties for primality testing and analyzes their effectiveness and limitations.

Findings

New algorithms for primality testing are proposed.

Invariant properties provide additional insights into factorization.

Advantages and disadvantages of these algorithms are discussed.

Abstract

The purpose of this article is to delve into the properties of invariants. The properties, explained in [2], reveal new ways to develop algorithms that allow us to test the primality of a number. In this article, some of these are shown, indicating the advantages and disadvantages of these new algorithms. The information provided by these algorithms also gives additional information regarding the factorization of a compound number.