A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories

M. Abdel-Mageed, Ahmed Salim, Walid Osamy and Ahmed M. Khedr

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

Abstract: 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 χ2 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.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2021/9956518

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:9956518

Access Statistics for this article

More articles in Advances in Mathematical Physics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().