# 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.

## Key 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".