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

Srikanth Cherukupally

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.

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

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.
Paper Structure (2 sections, 4 theorems, 14 equations)

This paper contains 2 sections, 4 theorems, 14 equations.

Table of Contents

  1. Introduction
  2. Sequence of arithmetic progressions

Key Result

Lemma 1

For a given $A(a,d)$ with $a$ and $d$ being co-prime, there exists only one progression $A(a',d')$ with $1\leq d' \leq d$ such that the terms of the two progressions are connected by Property $\mathcal{P}$.

Theorems & Definitions (9)

  • Lemma 1
  • proof
  • Definition 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 1
  • proof