Theorems on twin primes-dual case

TL;DR

This paper introduces and studies twin numbers of the second kind, proving their infinitude, and explores related conjectures and axiomatic concepts, expanding the theory of twin primes and their duals.

Contribution

It presents new theorems on twin numbers of the second kind, including proofs of their infinity and conditions for related postulates, advancing twin prime research.

Findings

Proof of the infinity of twin numbers of the second kind

A sufficient condition for the truth of the postulate

Introduction of a new axiom concept 'AiB'

Abstract

We prove dual theorems to theorems proved by author in \cite {5}. Beginning with Section 10, we introduce and study so-called "twin numbers of the second kind" and a postulate for them. We give two proofs of the infinity of these numbers and a sufficient condition for truth of the postulate; also we pose several other conjectures. Finally, we consider a conception of axiom of type "AiB".