Twin Primes and the Zeros of the Riemann Zeta Function

TL;DR

This paper explores the connection between twin primes and the zeros of the Riemann zeta function, offering new insights into their distribution and implications for the twin prime conjecture.

Contribution

It reworks the counting function of twin primes using the inverse Riemann zeta function, linking prime distribution to zeta zeros.

Findings

Provides a new analytical relation involving twin primes and zeta zeros

Offers insights into the distribution of zeta zeros in the critical strip

Suggests potential implications for the twin prime conjecture

Abstract

The Legendre type relation for the counting function of ordinary twin primes is reworked in terms of the inverse of the Riemann zeta function. Its analysis sheds light on the distribution of the zeros of the Riemann zeta function in the critical strip and their links to primes and the twin prime problem.