Riemann’s Hypothesis and Critical Line of Prime Numbers

Mazurkin Peter Matveevich

doi:doi:10.11648/j.ash.20150101.12

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Riemann’s Hypothesis and Critical Line of Prime Numbers

Mazurkin Peter Matveevich

Received: 20 July 2015 Accepted: 31 July 2015 Published: 1 August 2015

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Abstract

The binary numeral system is applied to the proof of a hypothesis of Riemann to a number of prime numbers. On the ends of blocks of a step matrix of binary decomposition of prime numbers are located a reference point. Because of them there is a jump of a increment of a prime number. The critical line and formula for its description is shown, interpretation of mathematical constants of the equation is given. Increment of prime numbers appeared an evident indicator. Increment is a quantity of increase, addition something. If a number of prime numbers is called figuratively "Gauss-Riemann's ladder", increment can assimilate to the steps separated from the ladder. It is proved that the law on the critical line is observed at the second category of a binary numeral system. This model was steady and at other quantities of prime numbers. Uncommon zero settle down on the critical line, and trivial – to the left of it. There are also lines of reference points, primary increment and the line bending around at the left binary number. Comparison of ranks of different power is executed and proved that the critical line of Riemann is only on the second vertical of a number of prime numbers and a number of their increments.

DOI	10.11648/j.ash.20150101.12
Published in	Advances in Sciences and Humanities (Volume 1, Issue 1, August 2015)
Page(s)	13-29
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Prime Numbers, Complete Series, Increment, Critical Line, Root 1/2

References

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APA Style

Mazurkin Peter Matveevich. (2015). Riemann’s Hypothesis and Critical Line of Prime Numbers. Advances in Sciences and Humanities, 1(1), 13-29. https://doi.org/10.11648/j.ash.20150101.12

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ACS Style

Mazurkin Peter Matveevich. Riemann’s Hypothesis and Critical Line of Prime Numbers. Adv. Sci. Humanit. 2015, 1(1), 13-29. doi: 10.11648/j.ash.20150101.12

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Mazurkin Peter Matveevich. Riemann’s Hypothesis and Critical Line of Prime Numbers. Adv Sci Humanit. 2015;1(1):13-29. doi: 10.11648/j.ash.20150101.12

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@article{10.11648/j.ash.20150101.12,
  author = {Mazurkin Peter Matveevich},
  title = {Riemann’s Hypothesis and Critical Line of Prime Numbers},
  journal = {Advances in Sciences and Humanities},
  volume = {1},
  number = {1},
  pages = {13-29},
  doi = {10.11648/j.ash.20150101.12},
  url = {https://doi.org/10.11648/j.ash.20150101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ash.20150101.12},
  abstract = {The binary numeral system is applied to the proof of a hypothesis of Riemann to a number of prime numbers. On the ends of blocks of a step matrix of binary decomposition of prime numbers are located a reference point. Because of them there is a jump of a increment of a prime number. The critical line and formula for its description is shown, interpretation of mathematical constants of the equation is given. Increment of prime numbers appeared an evident indicator. Increment is a quantity of increase, addition something. If a number of prime numbers is called figuratively "Gauss-Riemann's ladder", increment can assimilate to the steps separated from the ladder. It is proved that the law on the critical line is observed at the second category of a binary numeral system. This model was steady and at other quantities of prime numbers. Uncommon zero settle down on the critical line, and trivial – to the left of it. There are also lines of reference points, primary increment and the line bending around at the left binary number. Comparison of ranks of different power is executed and proved that the critical line of Riemann is only on the second vertical of a number of prime numbers and a number of their increments.},
 year = {2015}
}

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TY - JOUR
T1 - Riemann’s Hypothesis and Critical Line of Prime Numbers
AU - Mazurkin Peter Matveevich
Y1 - 2015/08/01
PY - 2015
N1 - https://doi.org/10.11648/j.ash.20150101.12
DO - 10.11648/j.ash.20150101.12
T2 - Advances in Sciences and Humanities
JF - Advances in Sciences and Humanities
JO - Advances in Sciences and Humanities
SP - 13
EP - 29
PB - Science Publishing Group
SN - 2472-0984
UR - https://doi.org/10.11648/j.ash.20150101.12
AB - The binary numeral system is applied to the proof of a hypothesis of Riemann to a number of prime numbers. On the ends of blocks of a step matrix of binary decomposition of prime numbers are located a reference point. Because of them there is a jump of a increment of a prime number. The critical line and formula for its description is shown, interpretation of mathematical constants of the equation is given. Increment of prime numbers appeared an evident indicator. Increment is a quantity of increase, addition something. If a number of prime numbers is called figuratively "Gauss-Riemann's ladder", increment can assimilate to the steps separated from the ladder. It is proved that the law on the critical line is observed at the second category of a binary numeral system. This model was steady and at other quantities of prime numbers. Uncommon zero settle down on the critical line, and trivial – to the left of it. There are also lines of reference points, primary increment and the line bending around at the left binary number. Comparison of ranks of different power is executed and proved that the critical line of Riemann is only on the second vertical of a number of prime numbers and a number of their increments.
VL - 1
IS - 1
ER -

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Author Information

Mazurkin Peter Matveevich

Department of Environmental Engineering, Volga State University of Technology, Yoshkar-Ola, Republic of Mari El, Russian Federation

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APA Style

Mazurkin Peter Matveevich. (2015). Riemann’s Hypothesis and Critical Line of Prime Numbers. Advances in Sciences and Humanities, 1(1), 13-29. https://doi.org/10.11648/j.ash.20150101.12

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ACS Style

Mazurkin Peter Matveevich. Riemann’s Hypothesis and Critical Line of Prime Numbers. Adv. Sci. Humanit. 2015, 1(1), 13-29. doi: 10.11648/j.ash.20150101.12

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AMA Style

Mazurkin Peter Matveevich. Riemann’s Hypothesis and Critical Line of Prime Numbers. Adv Sci Humanit. 2015;1(1):13-29. doi: 10.11648/j.ash.20150101.12

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@article{10.11648/j.ash.20150101.12,
  author = {Mazurkin Peter Matveevich},
  title = {Riemann’s Hypothesis and Critical Line of Prime Numbers},
  journal = {Advances in Sciences and Humanities},
  volume = {1},
  number = {1},
  pages = {13-29},
  doi = {10.11648/j.ash.20150101.12},
  url = {https://doi.org/10.11648/j.ash.20150101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ash.20150101.12},
  abstract = {The binary numeral system is applied to the proof of a hypothesis of Riemann to a number of prime numbers. On the ends of blocks of a step matrix of binary decomposition of prime numbers are located a reference point. Because of them there is a jump of a increment of a prime number. The critical line and formula for its description is shown, interpretation of mathematical constants of the equation is given. Increment of prime numbers appeared an evident indicator. Increment is a quantity of increase, addition something. If a number of prime numbers is called figuratively "Gauss-Riemann's ladder", increment can assimilate to the steps separated from the ladder. It is proved that the law on the critical line is observed at the second category of a binary numeral system. This model was steady and at other quantities of prime numbers. Uncommon zero settle down on the critical line, and trivial – to the left of it. There are also lines of reference points, primary increment and the line bending around at the left binary number. Comparison of ranks of different power is executed and proved that the critical line of Riemann is only on the second vertical of a number of prime numbers and a number of their increments.},
 year = {2015}
}

Copy | Download