Applied Physics and Mathematics Annotation << Back SOME QUESTIONS OF PROBABILISTIC NUMBER THEORY V.L. VOLFSON Recently, with the development of computer technology and the Internet, the problem of the distribution of prime numbers has acquired great practical importance, since it is directly related to the reliability of the so-called public key cryptographic systems. For example, the cryptographic strength of the currently widely used RSA encryption system is based on the computational complexity of factoring large natural numbers into prime factors. One of the questions of distribution of prime numbers is considered. It is shown what error is obtained from the assumption that the asymptotic density of a sequence of primes is a probability. Various forms of an analogue of the law of large numbers for arithmetic functions and, in particular, the Hardy-Ramunajan theorem are obtained. A method is given for finding the asymptotics of the probabilistic characteristics of arithmetic functions. Keywords: density of a subset of natural series, probability space, independent events, asymptotic density, asymptotic law of prime numbers, sieve of Eratosthenes, Mertens theorem, arithmetic function, Chebyshev inequality, analogue of the law of large numbers, strongly additive arithmetic function, limit distribution function, standard function normal distribution, asymptotics of probabilistic characteristics of arithmetic functions, sequence of random variables, independence of random variables, number of prime divisors of natural number. DOI: 10.25791/pfim.01.2021.1191 Pp. 38-45.