Applied Physics and Mathematics Annotation << Back THE DISTRIBUTION OF PRIME NUMBERS AND TUPLES IN THE NATURAL NUMBERS V.L. VOLFSON The probabilistic models of distribution of primes is one of the applications of the theory of probability. The paper considers the third probabilistic model of the distribution of primes in the natural number. The author proved – the results obtained by considering three probabilistic models are similar. It is shown – the accuracy of these probabilistic models exceeds the Riemann hypothesis with a certain probability. The results tested on a large volume of statistics. The author constructed probabilistic models for the analysis of the average distance between neighboring prime numbers and k-tuples. It is found the probability distributions of these random variables. The estimates of these random variables are obtained based on these probabilistic models. The resulting estimates are checked on a large volume of statistical data. Keywords: probabilistic model, random variable, probability estimates, primes, k-tuple, distribution of prime numbers, the distribution of prime k-tuples, Hardy and Littlewood conjecture, Riemann conjecture. Contacts: E-mail: znakvicvolf@mail.ru Pp. 09-15.