Science and Education Publishing
Applied Mathematics and Physics
2
4
2014
08
10
Chaos and Order in the Integers Primes
146
156
EN
P.M.
Mazurkin
Doctor of Engineering Science, Academician of RANS, member of EANS, Volga State University of Technology, Russia
AMP2014244
10.12691/amp-2-4-4
2014
08
05
2014
08
08
2014
08
10
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.