Three theorems on twin primes

Abstract

For earlier considered our sequence A166944 in [4] we prove three statements of its connection with twin primes. We also give a sufficient condition for the infinity of twin primes and pose several new conjectures; among them we propose a very simple conjectural algorithm of constructing a pair $(p,p+2)$ of twin primes over arbitrary given integer $m\ge 4$ such that $p+2\ge m.$

17 pages. New section: "A theorem on twin primes which is independent on observation of type 6)"

References in corpus (1)

• Generalizations of the Rowland theorem

Cited by in corpus (2)

• 10 conjectures in additive number theory
• Theorems on twin primes-dual case