Abstract
The article considers the generalized Artin's hypothesis. The analysis of algebraic dynamical systems on the set of prime numbers is given. The properties of dynamic algebraic systems are studied.Based on computer modeling, a solution of Artin’s generalized hypothesis was constructed. A classification of prime numbers for any natural number a 1 is constructed. The properties of classes of prime numbers are investigated. A method of structural analysis of algebraic dynamical systems with close values of generalized Artin constants was developed. It is established that for any a 1 each class has a probability measure, and the sum of the measures of the classes tends to unity.
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