PRIME NUMBERS: AN ALTERNATIVE STUDY USING OVA-ANGULAR ROTATIONS

Yeisson Alexis Acevedo Agudelo

doi:10.17654/nt052010127

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.

Highlights

IntroductionFrom functional analysis and number theory, direct contributions towards the study of prime numbers have been provided [1,2,3,4,5,6]
From functional analysis and number theory, direct contributions towards the study of prime numbers have been provided [1,2,3,4,5,6]. These contributions have linked the use of multiplicative functions, bounded sets, infimum, and supremum, as well as the importance of the norm and the modular congruences to establish differences or limit distances between consecutive primes, obtaining interesting results such as by Zhang, who established an important dimension for the distance of consecutive primes [7, 8]
It should be clarified that if the ova-angular rotation circle is positioned in any integer belonging to the interval [(n + 1)! + 2, (n + 1)! + n + 1] it has not a prime number, it will not be an object of interest, it will only rotate

Summary

Introduction

From functional analysis and number theory, direct contributions towards the study of prime numbers have been provided [1,2,3,4,5,6]. Addressing integer modules, quantities of prime numbers, and arithmetic progressions, he establishes his theorem "About primes in arithmetic progressions" [9] With his theorem, Dirichlet presents the possibility of classifying the prime numbers according to their residue modulo n, with integer n. A further interpretation of this theorem is developed and it is established that among all the possible integer modules that can be established to generate progressions with infinite prime numbers, the one that presents more stability is the 360 module. This development is induced at a theoretical level under the denomination ova-angular rotations. Adding the elements that provide ova-angular rotations and their applications within the field of mathematics could bring closer to reality the idea that both physics and mathematics are closely related and there is a constitutional relationship between these knowledge sciences [10, 11]

Introduction to Ova-angular Rotations of a Prime Number

Geometry

Aplications

Conclusions