On the distribution of composite odd numbers

TL;DR

This paper investigates the distribution of odd numbers, especially primes and composites, using indexing and counting arguments to analyze the convergence of related sums.

Contribution

It introduces a novel indexing approach and analyzes the convergence rates of sums related to odd primes and composites.

Findings

Calculated limits of two sums involving odd numbers

Compared convergence rates of these sums

Provided insights into the distribution patterns of odd primes and composites

Abstract

We study odd numbers through a straightforward indexing. We focus in particular on odd prime and composite numbers and their distribution. With a counting argument, we calculate the limit of two sums and compare their convergence rate.