The Infinitude of Twin Primes

Abstract

The twin prime conjecture inquires whether there are infinitely many prime (p) pairs of the form (p, p+2). This longstanding problem remains unresolved in number theory. Although the infinitude of prime numbers has been rigorously established, the question of infinitely many twin prime pairs has proven considerably more challenging as numerous proposed proofs have been refuted upon closer examination. In this paper, twin primes are classified into three categories according to their final digit. Patterns arising within each category are analyzed, and a proof addressing the infinitude of twin primes is presented.