The Goldbach’s Conjecture is an astonishing proposition that stands as one of the most renowned and enduring unsolved problems in number theory and mathematics. This research aims to provide a proof for this remarkable conjecture. The approach to be followed for the proof is yielded by using a predefined system of equations, and with a relatively simple analysis. The proof is quite simple compared to the size of the problem. In the second part of this study, we leverage the same system of equations to develop a general mathematical framework for predicting prime numbers within the known sequence, laying down a general mathematical framework that is computationally concise and can just achieve the objective. With proper selection of the coefficients of the equations in the algorithm, it’s guaranteed that prime numbers are among the outputs. The algorithm consists of basic arithmetic operations which is by itself ground breaking. The proof of the algorithm is also astoundingly straightforward and compact.