Towards Proving the Twin Prime Conjecture using a Novel Method For Finding the Next Prime Number ${P_{N+1}}$ after a Given Prime Number ${P_{N}}$

This paper proposes an alternative method to find the next prime number after a given prime ${P}$. The proposed mathematical formula is used to derive certain inequalities, which are then proposed as constraints that should be satisfied by all primes that are followed by a twin as the next prime number. Twin primes are primes that have a prime gap of ${2}$. The pairs ${(5,7),(11,13),(41,43)}$, etcetera are all twin primes. Each number in these pairs is also called a twin prime. This paper envisions that if the proposed system of inequalities can be proven to have infinite solutions, the Twin Prime Conjecture will evidently be proven true.