New conjectures in number theory - The distribution of prime numbers

TL;DR

This paper explores the distribution of prime numbers, proposing new conjectures and methods to understand their spacing, including bounds for the primes counting function and approaches to Legendre's conjecture.

Contribution

It introduces novel conjectures and an iterative method to analyze prime distribution, aiming to resolve longstanding questions about prime gaps and density.

Findings

Proposes a new lower bound for the primes counting function

Provides an estimate related to Legendre's conjecture

Introduces an iterative method for solving equations in number theory

Abstract

Since the mathematicians of ancient Greece until Fermat, since Gauss until today; the way how the primes along the numerical straight line are distributed has become perhaps the most difficult math problem; many people believe that their distribution is chaotic, governed only by the laws of chance. In this article the author tries to resolve satisfactorily all matter related to the distance between primes, based on the determination of a lower bound for the primes counting function, the estimate of Legendre's conjecture, and the iterative method for solving equations.