**Structure of Prime Numbers' Distribution**

1.
Groups of Prime Numbers'
Differences

This
paper reports some results of experimental investigation on computer prime numbers
in the range until 1 billion.

It has been detected that gaps between consecutive gaps (second differences of
primes), named variations, constitute regular and repeating irregular groups.
Maximal size of such a group of every type of them depends on 4 special
characteristics of each type. All numbers constituting maximal sizes of such
groups exist in 2 geometrical figures - hexagram and pentagram.

Besides, as a range of primes increased, the ratio of the number of repeating
groups of 2 consecutive variations to the number of primes in the range aspires
to 100%.

Chart of gaps in the range of primes until
10,000

__Lists
of variations' groups:__

Regular (symmetrical) groups in the range of primes until 1,000,000

Symmetriads S2, S3, S4, S5, S6, S8, and S10

Curls C3, C4, C5, C6, C7, C8, C9, and C10

Flats F2 and F3

Repeating irregular (asymmetrical) groups in the range of primes until 100,000

Any Q2, Q3, Q4, Q5, Q6, Q7, Q8, Q9, Q10, Q11, and Q12

Independent Qi2, Qi3, Qi4, Qi5, Qi6, Qi7, Qi8, Qi9, Qi10, and Q12

2.
Classes
of Prime Numbers and Their Differences

In this
paper, the author discusses primes' and their differences' classes on the base
of 6. These classes are of importance in distribution values of differences of
primes, as the first ones, gaps, as the second ones, variations.

The main reason of six period oscillations in distributions
both gaps and variations and the peculiarity of each of them is the
distribution of primes themselves in groups of the same class. Besides, in such
an oscillation in exponent distribution of variations values, the numbers
determining the class of each a variation on the same base play an essential
role.

An analytical research of a problem of independent appearing
of a next prime of the same class as of a current one or of the opposite class
proves it possible in the in infinite general set of prime numbers only.