Primes Distribution Linearity. Composite Numbers Cyclicity. Chaoticity of Primes. Twin Primes Occurrence

TL;DR

This paper presents a linear framework suggesting all primes lie on specific half-lines, with composite numbers outside these lines, and reveals cyclical patterns in the distribution of composite numbers within natural numbers.

Contribution

Introduces a linear relationship that characterizes prime numbers and demonstrates cyclical patterns in composite number distribution.

Findings

All primes lie on 96 half-lines.

Composite numbers do not satisfy the linear relation.

Cyclical patterns observed in composite number occurrence.

Abstract

In this paper it was shown that all prime numbers lie on 96 half-lines. At the same time, it was shown that if a given number does not lie on any of the above half-lines, then it is a composite number. A corresponding linear mathematical relationship was also derived and it was shown that all prime numbers must satisfy it. If a given number does not satisfy the above dependence, then it is a composite number. One linear equation and 8 numbers are enough to carry out all of the above-mentioned analyses. In addition, the astonishing cyclical nature of the occurrence of composite numbers in the set of natural numbers has been demonstrated.