An Equivalent form of Twin Prime Conjecture connected with a sequence of arithmetic progressions

TL;DR

This paper presents an equivalent formulation of the Twin Prime Conjecture based on a symmetric property observed in a specific sequence of arithmetic progressions related to co-prime integers.

Contribution

It introduces a new equivalent form of the Twin Prime Conjecture linked to properties of arithmetic progressions and co-prime pairs, offering a different perspective on the problem.

Findings

Identifies a symmetric property in arithmetic progressions.

Establishes an equivalent form of the Twin Prime Conjecture.

Provides insights into the structure of primes in specific sequences.

Abstract

We give an equivalent form of the Twin prime conjecture relating to a symmetric property that is observed for terms present in a certain sequence of arithmetic progressions defined for a pair of co-prime integers.