Distribution law for twin primes amongst naturals

TL;DR

This paper proposes a hypothesis about the distribution of twin primes among natural numbers, introduces an empirical function to model this distribution, and demonstrates its high accuracy through evaluation.

Contribution

It introduces a new hypothesis and an empirical function for twin prime distribution, providing a highly accurate model based on evaluation.

Findings

Empirical function $^{\u2212}$(x) accurately models twin prime distribution

The hypothesis offers new insights into twin prime distribution patterns

Several related questions about twin primes are addressed

Abstract

A hypothesis is put forward regarding the function $\pi_2(x)$ which describes the distribution of twin primes in the set of natural numbers. The function $\pi_2(x)$ is tested by evaluation and an empirical $\pi_2^{\ast}(x)$ is arrived at, which is shown to be highly accurate. Several other questions are also addressed.