A study on the statistical properties of the prime numbers using the classical and superstatistical random matrix theories
type: Item
instance of: scholarly article
title: A study on the statistical properties of the prime numbers using the classical and superstatistical random matrix theories
zbMATH Open document ID: 1475.11163
DOI: 10.1155/2021/9956518
author: M. Abdel-Mageed
author: Ahmed Salim
author: Walid Osamy
author: Ahmed M. Khedr
published in: Advances in Mathematical Physics
publication date: 2021-11-25T00:00:00Z
review text: Summary: The prime numbers have attracted mathematicians and other researchers to study their interesting qualitative properties as it opens the door to some interesting questions to be answered. In this paper, the Random Matrix Theory (RMT) within superstatistics and the method of the Nearest Neighbor Spacing Distribution (NNSD) are used to investigate the statistical proprieties of the spacings between adjacent prime numbers. We used the inverse \(\chi^2\) distribution and the Brody distribution for investigating the regular-chaos mixed systems. The distributions are made up of sequences of prime numbers from one hundred to three hundred and fifty million prime numbers. The prime numbers are treated as eigenvalues of a quantum physical system. We found that the system of prime numbers may be considered regular-chaos mixed system and it becomes more regular as the value of the prime numbers largely increases with periodic behavior at logarithmic scale.
Mathematics Subject Classification ID: 11N05
Mathematics Subject Classification ID: 60B20
zbMATH DE Number: 7433524
zbMATH Keywords: superstatistical random matrix theories
zbMATH Keywords: nearest neighbor spacing distribution
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/9956518
OpenAlex ID: W3200605204
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description: scientific article; zbMATH DE number 7433524