Probabilistic methods in computer simulation of the formation of classes of primes and estimation of the constants of the generalized Artin hypothesis

Abstract

The relationship between the processes of forming classes of primes in the generalized Artin hypothesis based on the theory of randomized algorithms of the probabilistic method is investigated. It is proved that probabilistic methods are the basis for constructing computer models of classes of primes in accordance with the generalized Artin hypothesis. Methods for calculating the Artin constants are developed and the convergence of the estimates of the constants in probability to the limiting values is established. The foundations of a number-theoretic analysis of Artin's constants and related classes are created.