Subsets of prime numbers in the generalized arithmetical progressionsAbstract
The concept of the generalized arithmetical progression of the power k and difference d is given. For k 1,7 formulas of nth member of such 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 d for 2 k 60, p 1014, h 5 are established.