Generalized Twin Prime Formulas

TL;DR

This paper constructs Dirichlet series for twin primes based on Golomb's formulas and explores their connection to the Riemann zeta function's roots, advancing understanding of twin prime distribution.

Contribution

It introduces generalized formulas for twin primes and links them to the Riemann zeta function, providing new analytical tools for prime number research.

Findings

Dirichlet series for twin primes are constructed.

Connections between twin prime formulas and zeta function roots are established.

Potential implications for twin prime conjecture are discussed.

Abstract

Based on Golomb's arithmetic formulas, Dirichlet series for two classes of twin primes are constructed and related to the roots of the Riemann zeta function in the critical strip.