Accurate and Infinite Prime Prediction from Novel Quasi-Prime Analytical Methodology

TL;DR

This paper introduces a novel deterministic method based on geometric patterns and digital roots to accurately predict prime numbers and factors, eliminating the need for trial division or probabilistic approaches.

Contribution

It presents a new analytical approach linking geometric moduli and digital roots to prime prediction, highlighting the 24-sided polygon's unique role in prime distribution.

Findings

Prime numbers follow specific geometric moduli patterns.

Non-prime numbers sharing these moduli have unique properties.

The method predicts primes accurately without trial division.

Abstract

It is known that prime numbers occupy specific geometrical patterns or moduli when numbers from one to infinity are distributed around polygons having sides that are integer multiple of number 6. In this paper, we will show that not only prime numbers occupy these moduli, but non-prime numbers sharing these same moduli have unique prime-ness properties. When utilizing digital root methodologies, these non-prime numbers provide a novel method to accurately identify prime numbers and prime factors without trial division or probabilistic-based methods. We will also show that the icositetragon (24-sided regular polygon) is a unique polygon pertaining to prime numbers and their ultimate incidence and distribution.