STATISTICAL AND ALGEBRAIC PROPERTIES OF THE DISTRIBUTION OF PRIMITIVE ROOTS IN SETS OF CONSECUTIVE PRIMES
Abstract
The justification of the necessity of full qualitative information about the algebraic properties of primitive roots in the sets of consecutive primes is given, taking into account the area of their location in the set of all primes and its cardinality. It is proven that with a significant deepening of the location of the set ( 1)p of consecutive primes, the value of smoothly but systematically increases to such an extent that at a certain stage of the deepening process the average distance between the primitive roots of such sets of consecutive primes smoothly increases to a certain extent. The foundations of mathematical estimation of the entropy of probabilities of changes in the statistical properties of the mathematical expectation of the
average distance between the primitive roots are developed. The methods of computer modeling of processes of formation of statistical laws of distribution of primitive roots in such systems of consecutive prime numbers ofsignificant power are created.