Applied Mathematics and Physics
ISSN (Print): 2333-4878 ISSN (Online): 2333-4886 Website: http://www.sciepub.com/journal/amp Editor-in-chief: Vishwa Nath Maurya
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Applied Mathematics and Physics. 2014, 2(4), 146-156
DOI: 10.12691/amp-2-4-4
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Chaos and Order in the Integers Primes

P.M. Mazurkin1,

1Doctor of Engineering Science, Academician of RANS, member of EANS, Volga State University of Technology, Russia

Pub. Date: August 10, 2014

Cite this paper:
P.M. Mazurkin. Chaos and Order in the Integers Primes. Applied Mathematics and Physics. 2014; 2(4):146-156. doi: 10.12691/amp-2-4-4

Abstract

Statistical modeling by asymmetric waves, with variables amplitude and a half-cycle of fluctuation, dynamics of a scatter of block structure of positive part of a number of the integers prime which located in a row of 10 million natural numbers, proved emergence of three stages of growth of the left and right reference points in blocks of binary decomposition of prime numbers. These a reference point settle down on each side from the dividing line in the form of the two in the degree equal to number of the category of a binary numeral system, without unit. The first stage of critical chaos is formed by critical prime numbers 0, 1 and 2. The second stage of an accruing order begins with number 3 and comes to the end with a margin error in 1% at the 1135th category of binary notation for the left reference point. At blocks increasing on length among the integers prime by calculations after the 1135th category there comes the third stage with high definiteness of the beginning and the end of blocks of binary decomposition of positive prime numbers.

Keywords:
integers prime positive part binary representation blocks a reference point the dividing line three stages of the critical chaos an accruing order and high definiteness.

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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References:

[1]  I.N. Beckman, “Informatics. Course of lectures.” URL: http://profbeckman.narod.ru/InformLekc.htm
 
[2]  P.M. Mazurkin. “Patterns of primes”. Germany: Palmarium Academic Publishing, 2012. 280 p.
 
[3]  P.M. Mazurkin, “Series Primes in Binary.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 2 (2014): 60-65.
 
[4]  P.M. Mazurkin, “Proof the Riemann Hypothesis.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 1 (2014): 53-59.
 
[5]  P.M. Mazurkin, “Increment Primes.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 2 (2014): 66-72.