Dynamic Structure of Prime Numbers Distribution

Comparing  consecutive gaps between prime numbers, 

a lot of new regularities hidden in the chaos of the distribution

 of these marvelous numbers have been discovered

Primes and gaps + variations

 

 

Groups of Prime Numbers' Second Differences:
Introduction of variations explains what is the reason to go to the next,  more profound, step in dynamic structure of primes
Regular and repeating irregular groups  of consecutive variations in the range 
of primes until 1,000,000,000
Maximal sizes of regular and repeating irregular groups  depend on dynamic characteristics of each type of them
Groups in the range
until 100,000
statistics of repeating groups
of consecutive variations
Groups in the range
until 1,000,000
statistics of repeating and regular groups
of consecutive variations

Appendix

 

 

Classes of Prime Numbers and Their Differences:

Key of primes is number 6
Distributions of gaps and variations show six period oscillations 
Boolean algebra of classes of primes from 7, gaps, and variations 
Consecutive primes can be of any class independently in the infinite general primes' set
Distribution of groups of primes of the same class in the infinite general set in consequence of appearing consecutive primes of any class independently
Distribution of groups of primes of the same class in the finite range statistics and analysis differences from that in the infinite general set

 

 

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Last updated 03/11/2009
Copyright 2003 Michael Chassis. All rights reserved.