The Proof of the Twin-Prime Conjecture

A twin prime is a pair of prime numbers separated by a gap of two. Twin primes are more common when the prime numbers themselves are small but become increasingly rare when the prime numbers are larger. Furthermore, it is unknown whether there are infinitely many twin primes. In particular, the famous twin prime conjecture claims that there exist infinitely many twin primes. The importance of the conjecture lies in its simplicity and ubiquity, since verifying or refuting it would revolutionize our understanding of the behavior of primes with practical implications in such fields as number theory and cryptography. The conjecture is easy to understand and explain. However, it remains one of the most challenging, previously unsolved, problems in mathematics. Although recent contributions of Yitang Zhang, James Maynard, Terence Tao and many others have progressed in getting closer towards proving the conjecture, at present, it is still unsolved. Hence, to investigate this problem, in this paper, we propose a novel approach to theoretically validate the twin prime conjecture.