Results: **3**

#### About one way of determination of prime numbers

The method of finding prime numbers without computer calculation is shown. **Subsets** P1 = {6k1 – 1}, P2 = {6k2 + 1}, Q1 = {6j1 – 1}, Q2 = {6j2 + 1} are considered, where P1 È P2 are all prime numbers p ≥ 5; Qi are all odd composite numbers of such form. **Subsets** Ai = {ki}, Bi = {ji} (i = 1, 2) are investigated. It is proved ...

#### About some regularities in a structure of **subsets** of prime numbers

It is shown that the first four primes 2, 3, 5, 7 generate finite **subsets** of primes, assuming the principle of interchangeability. In is established that any prime p(11 p 41, p 19), added together with two preceding primes generates a prime and that any prime p (5 p 31, p 13), added together with two consequent ...

**Subsets** of prime numbers in the generalized arithmetical progressions

... and for k 1, 2, 3 formulas for the sum of the first n its members are obtained. Progressions ( ) , k p d M with the first member prime number p and difference being a positive even number d 2m (m ) are considered. Such progressions define **subsets** ( )
, , k h p d M of h prime numbers (h ). For k 20, p 95467, d 108 all **subsets** (1) h,p,d M with h 15 prime numbers are obtained. Some properties that connect the power k of generalized arithmetical progression and its difference ...