
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 ...

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 ...

Mathematical model of under control system describing by homogeneous Markov process
Complex systems are investigated by partitioning of set of conditions into subsets of under control and not under control conditions. Probabilities of the events connected with stay of casual process in these sets, and probabilities of transition from one subset to another are considered.
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Ширяев А. Н.
Вероятность: ...