A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories
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 Spaci...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/9956518 |
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| author | M. Abdel-Mageed Ahmed Salim Walid Osamy Ahmed M. Khedr |
| author_facet | M. Abdel-Mageed Ahmed Salim Walid Osamy Ahmed M. Khedr |
| author_sort | M. Abdel-Mageed |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e8087516989a41bb8f8cab964f2f36e4 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-e8087516989a41bb8f8cab964f2f36e42025-02-03T05:47:37ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/99565189956518A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix TheoriesM. Abdel-Mageed0Ahmed Salim1Walid Osamy2Ahmed M. Khedr3Department of Physics, Unaizah College of Science and Arts, Qassim University, Qassim, Saudi ArabiaFaculty of Science, Zagazig University, Zagazig, EgyptDepartment of Applied Natural Science, College of Community, Qassim University, Unaizah, Saudi ArabiaFaculty of Science, Zagazig University, Zagazig, EgyptThe 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.http://dx.doi.org/10.1155/2021/9956518 |
| spellingShingle | M. Abdel-Mageed Ahmed Salim Walid Osamy Ahmed M. Khedr A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories Advances in Mathematical Physics |
| title | A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories |
| title_full | A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories |
| title_fullStr | A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories |
| title_full_unstemmed | A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories |
| title_short | A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories |
| title_sort | study on the statistical properties of the prime numbers using the classical and superstatistical random matrix theories |
| url | http://dx.doi.org/10.1155/2021/9956518 |
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