SYSTEMATIC ANALYSIS OF THE DISTRIBUTION OF PRIMITIVE ROOTS OF PRIME NUMBERS IN ARTIN’S CONJECTURE

Abstract

The results of the study of the laws of distribution of primitive roots of prime numbers p on sets of natural numbers and their connection with Artin's conjecture are presented. The systematic nature of the formation of classes of prime numbers and generalized constants is proven. A complete justification of the laws of formation of classes of prime numbers with a certain value of indices and the corresponding Artin constants is given. The regularities of the formation of Artin classes are found and it is proven that they depend on a significant number of factors related to the properties of the corresponding primes. The analysis of the factors is given and the regularities that significantly affect the processes of formation of the distribution of prime roots are investigated.