The distribution of prime numbers and tuples in the natural numbers

Abstract

We studied two probabilistic models of the distribution of primes in the natural number [1].The paper considers the third probabilistic model of the distribution of primes in the natural number. The author proved that the results obtained by considering three probabilistic models are similar. It is shown that the accuracy of these probabilistic models exceeds the Riemann hypothesis with a certain probability. The author constructed probabilistic models for the analysis of the average distance between neighboring prime numbers and k-tuples and found probability distributions of these random variables. The estimates of these random variables are obtained based on these probabilistic models. The resulting estimates tested on a large volume of statistical data.