STATISTICAL AND ALGEBRAIC PROPERTIES OF THE DISTRIBUTION OF PRIMITIVE ROOTS IN SETS OF CONSECUTIVE PRIMES

  • Георгій Миколайович Востров National University «Odesа Polytechnic» https://orcid.org/0000-0003-3856-5392
  • Роман Юрійович Опята National University «Odesа Polytechnic» https://orcid.org/0000-0001-5806-9615
  • Максим Олександрович Ставратій National University «Odesа Polytechnic»
  • Олександр Щербанюк National University «Odesа Polytechnic»
Keywords: distribution of primitive roots; Artin’s constants; classes of prime numbers; distribution of indices modulo prime; distances between primitive roots.

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.

Author Biographies

Георгій Миколайович Востров, National University «Odesа Polytechnic»

Ph. D. of Technical Sciences, Associate Professor of the
Department of Applied Mathematics and Information Technologies

Роман Юрійович Опята, National University «Odesа Polytechnic»

PhD student of the Department of Applied Mathematics and
Information Technologies

Максим Олександрович Ставратій, National University «Odesа Polytechnic»

undergraduate student of the Department of Applied
Mathematics and Information Technologies

Олександр Щербанюк, National University «Odesа Polytechnic»

graduate student of the Department of Applied
Mathematics and Information Technologies

Published
2022-10-16
How to Cite
Востров, Г., Опята, Р., Ставратій, М., & Щербанюк, О. (2022). STATISTICAL AND ALGEBRAIC PROPERTIES OF THE DISTRIBUTION OF PRIMITIVE ROOTS IN SETS OF CONSECUTIVE PRIMES. Electrotechnic and Computer Systems, (36 (112), 57-65. https://doi.org/10.15276/eltecs.36.112.2022.06
Section
Computer Systems, Networks and their Components

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