Version 1
: Received: 6 September 2024 / Approved: 6 September 2024 / Online: 6 September 2024 (12:07:54 CEST)
How to cite:
mousavi, S. K. The Distribution of Prime Numbers Based on the Proof of Riemann’s Hypothesis and the Properties of the Numbers 3, 6, and 9. Preprints2024, 2024090541. https://doi.org/10.20944/preprints202409.0541.v1
mousavi, S. K. The Distribution of Prime Numbers Based on the Proof of Riemann’s Hypothesis and the Properties of the Numbers 3, 6, and 9. Preprints 2024, 2024090541. https://doi.org/10.20944/preprints202409.0541.v1
mousavi, S. K. The Distribution of Prime Numbers Based on the Proof of Riemann’s Hypothesis and the Properties of the Numbers 3, 6, and 9. Preprints2024, 2024090541. https://doi.org/10.20944/preprints202409.0541.v1
APA Style
mousavi, S. K. (2024). The Distribution of Prime Numbers Based on the Proof of Riemann’s Hypothesis and the Properties of the Numbers 3, 6, and 9. Preprints. https://doi.org/10.20944/preprints202409.0541.v1
Chicago/Turabian Style
mousavi, S. K. 2024 "The Distribution of Prime Numbers Based on the Proof of Riemann’s Hypothesis and the Properties of the Numbers 3, 6, and 9" Preprints. https://doi.org/10.20944/preprints202409.0541.v1
Abstract
In this paper, the distribution of prime numbers is expressed based on proving the Riemann hypothesis. The modality to the distribution of prime numbers is one of the most important results of proving the Riemann hypothesis. The relationship between three numbers, three, six, and nine, and the modality to the distribution of prime numbers, is one of the results of Riemann's zeta function. Prime numbers are classified into six groups of single-digit numbers. There are no prime numbers in groups of three, six, and nine. The groups are made based on the sum of the internal digits. And for each set, there is an angle in the complex plane. The distance between the prime numbers in each group has a regular pattern. This pattern is a multiple of the numbers three, six, and nine. According to Euler's number, for an angle of 60 degrees, the real part of the cosine is 0.5. Accordingly, all prime numbers are related to angles greater than 60 degrees to 90 degrees. As a result, based on the relationship between the golden spiral and the complex conjugate of the zeta function, the function in The 1/2 point becomes zero.
Keywords
prime numbers; Riemann's hypothesis; three numbers 3; 6; 9
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
