Asymptotics of the number of primes and sums of functions of primes in a subset of natural series

TL;DR

This paper investigates the asymptotic behavior of the count and sum of primes within specific subsets of natural numbers that maintain a positive, constant density of primes, advancing understanding of prime distribution in structured subsets.

Contribution

It provides new asymptotic formulas for the number of primes and sums of functions of primes in subsets with positive prime density, under specified conditions.

Findings

Derived asymptotic formulas for prime counts in subsets

Established conditions for sums of functions of primes in these subsets

Enhanced understanding of prime distribution in structured natural number subsets

Abstract

The paper solves the problems of determining the asymptotics of the number of primes and the sums of functions of primes in a subset of the natural series that satisfies the conditions that the asymptotic density of the number of primes in this subset is constant and not equal to zero.