Riemann’s Hypothesis and Critical Line of Prime Numbers
Advances in Sciences and Humanities
Volume 1, Issue 1, August 2015, Pages: 13-29
Received: Jul. 20, 2015; Accepted: Jul. 31, 2015; Published: Aug. 1, 2015
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Mazurkin Peter Matveevich, Department of Environmental Engineering, Volga State University of Technology, Yoshkar-Ola, Republic of Mari El, Russian Federation
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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.
Prime Numbers, Complete Series, Increment, Critical Line, Root 1/2
To cite this article
Mazurkin Peter Matveevich, Riemann’s Hypothesis and Critical Line of Prime Numbers, Advances in Sciences and Humanities. Vol. 1, No. 1, 2015, pp. 13-29. doi: 10.11648/j.ash.20150101.12
N.M. Astafieva. Wavelet analysis: bases of the theory and application examples//Achievements of physical sciences. 1996. Volume 166, No. 11 (November). Page 1145-1170.
S.B. Gashkov. Numeral systems and their application. Moscow: Moscow Center of Continuous Mathematical Education, 2004. 52 pages.
P.M. Mazurkin. Asymmetric ranks of the whole prime numbers // Collection of scientific works SWorld. Release 3. Volume 4. Odessa: KUPRIENKO SV, 2013. DOI: 313-0468. Page 35-42.
P.M. Mazurkin. Biotechnical law and designing of adequate models // Achievements of modern natural sciences 2009. No. 9. Page 125-129.
P.M. Mazurkin. The biotechnical law, algorithm in intuitive sense and algorithm of search of parameters // Achievements of modern natural sciences. 009. No. 9. Page 88-92.
P.M. Mazurkin. The biotechnical principle in statistical modeling // Achievements of modern natural sciences. 2009 . No. 9. Page 107-111.
P.M. Mazurkin. Biotechnical principle and steady laws of distribution // Achievements of modern natural sciences. 2009. No. 9 of Page 93-97. URL: www.rae.ru/use/?section=content&op= show article&article_id=7784060.
P.M. Mazurkin. Regularities of prime numbers. Germany: Palmarium Academic Publishing, 2012. 280 pages.
P.M. Mazurkin. Increment of prime numbers // Modern high technologies. 2012. No. 10. Page 31-39.
P.M. Mazurkin. Increment of the whole prime numbers // Collection of scientific works SWorld. Release 3. Volume 4. Odessa: KUPRIENKO SV, 2013. DOI: 313-0468 . Page 43-48.
P.M. Mazurkin. Expanded proof of a hypothesis of Riemann // Modern high technologies. 2012 . No. 10. Page 40-47.
P.M. Mazurkin. The decision 23-oh Gilbert's problems // Interdisciplinary researches in the field of mathematical modeling and informatics. Materials of the 3rd scientific and practical internet-conference Ulyanovsk: SIMJET, 2014. Page 269-277.
P.M. Mazurkin. A number of prime numbers in binary system//Modern high technologies. 2012. No. 10. Page 23-30. Page 269-277.
P.M. Mazurkin. Steady laws and prime numbers // Basic researches. 2012 . No. 3. Page 106-112. http://www.rae.ru/fs/pdf/2012/3/21.pdf
P.M. Mazurkin. Whole prime numbers//International research magazine. No. 4(23). Part 1. Yekaterinburg: individual entrepreneur of Sokolov M.V., 2014. Page 17-24. https://app.box.com/s/npz2cldjfwad5wgoomjc
Mathematical constant. URL: http://ru.wikipedia.org/wiki/%D0%9C%D0%B0% D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D0%BA%D0%BE%D0%BD%D1%81%D1%82%D0%B0%D0%BD%D1%82%D0%B0
A.P. Stakhov. Metal Proportions – new mathematical constants of the Nature // "Trinitarizm's Academy". M.: Electronic No. 77-6567, 14748, 22.03.2008. URL: http://www.trinitas.ru/ rus/doc/0232/004a/02321079.htm
Gödel's theorem of incompleteness. URL: http://ru.wikipedia.org/wiki
D. Zahir. First 50 million prime numbers. URL: http://www.egamath.narod.ru/Liv/Zagier.htm.
P.M. Mazurkin, “Increment Primes.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 2 (2014): 66-72. doi: 10.12691/ajams-2-2-3.
P.M. Mazurkin, “Proof the Riemann Hypothesis.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 1 (2014): 53-59. doi: 10.12691/ajams-2-2-1.
P.M. Mazurkin, “Stable Laws and the Number of Ordinary.” Applied Mathematics and Physics, vol. 2, no. 2 (2014): 27-32. doi: 10.12691/amp-2-2-1.
P.M. Mazurkin, “Wavelet Analysis of a Number of Prime Numbers.” American Journal of Numerical Analysis, vol. 2, no. 2 (2014): 29-34. doi: 10.12691/ajna-2-2-1.
P.M. Mazurkin, “Series Primes in Binary.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 2 (2014): 60-65. doi: 10.12691/ajams-2-2-2.
Vera W. de Spinadel. From the Golden Mean to Chaos. Nueva Libreria, 1998 (second edition, Nobuko, 2004).
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