Open AccessOn some characteristics of subset of prime numbers
Author(s) -
V. S. Malakhovsky
Publication year - 2019
Publication title -
differencialʹnaâ geometriâ mnogoobrazij figur
Language(s) - English
Resource type - Journals
eISSN - 2782-3229
pISSN - 0321-4796
DOI - 10.5922/0321-4796-2019-50-12
Subject(s) - natural number , mathematics , combinatorics , set (abstract data type) , arithmetic , prime factor , arithmetic progression , discrete mathematics , prime number , prime (order theory) , computer science , programming language
The set of prime numbers p ≥ 5 is divided into two nonoverlapping subset P1 = {6k1 1}, P2 = {6k2 + 1}, where ki ⋲ A (i = 1,2). Subsets A1, A2 of natural numbers is defined by differences Ai = N\Bi, where B1, B2 are subset {j1}, {j2} defining subsets {6j1 – 1}, {6j2 + 1} of odd composite numbers. In [1] is proved two theorems permitting easily find by means of arithmetic progression subset Bi for ji a ⋲ N. The tables of numbers ki for a = 500 are defined and some characteristic of subsets P1, P2 are given.