Prime numbers. An alternative study using ova-angular rotations

TL;DR

This paper introduces ova-angular rotations of primes, exploring their geometric properties and applications to problems like Goldbach's conjecture, primes of the form k^2+1, and Mersenne primes, using elementary mathematics.

Contribution

It presents a novel geometric framework for prime numbers called ova-angular rotations and introduces the ova-angular square matrix, offering new insights into prime-related conjectures.

Findings

Analysis of ova-angular rotations of primes.

Applications to Goldbach's conjecture and primes of form k^2+1.

Convergence of sum of inverses of Mersenne primes.

Abstract

Ova-angular rotations of a prime number are characterized, constructed using the Dirichlet theorem. The geometric properties arising from this theory are analyzed and some applications are presented, including Goldbach's conjecture, the existence of infinite primes of the form $\rho = k^2+1$ and the convergence of the sum of the inverses of the Mersenne's primes. Although the mathematics that was used was elementary, you can notice the usefulness of this theory based on geometric properties. In this paper, the study ends by introducing the ova-angular square matrix.