Exceptional Prime Number Twins, Triplets and Multiplets

TL;DR

This paper classifies special twin primes and extends the concept to triplets and multiplets, revealing new exceptional prime configurations and their generalizations.

Contribution

It introduces a classification scheme for twin primes and derives new exceptional prime triplets and multiplets, expanding understanding of prime constellations.

Findings

Identification of special twin primes

Discovery of exceptional prime triplets

Generalization to prime multiplets

Abstract

A classification of twin primes implies special twin primes. When applied to triplets, it yields exceptional prime number triplets. These generalize yielding exceptional prime number multiplets.