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Riemann’s Hypothesis and Critical Line of Prime Numbers
Volume 1, Issue 1, August 2015, Pages: 13-29
Received: Jul. 20, 2015; Accepted: Jul. 31, 2015; Published: Aug. 1, 2015
Author
Mazurkin Peter Matveevich, Department of Environmental Engineering, Volga State University of Technology, Yoshkar-Ola, Republic of Mari El, Russian Federation
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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.
Keywords
Prime Numbers, Complete Series, Increment, Critical Line, Root 1/2
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
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