  This paper introduces a new method to find the next prime number after a
given prime ${P}$. The proposed method is used to derive a system of
inequalities, that serve as constraints which should be satisfied by all primes
whose successor is a twin prime. Twin primes are primes having a prime gap of
${2}$. The pairs ${(5,7),(11,13),(41,43)}$, etcetera are all twin primes. 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. The paper also derives a novel upper bound on the prime gap, ${G_{i}}$
between ${P_{i} \; and \; P_{i+1}}$, as a function of ${P_{i}}$.
