An Optimized Algorithm for the Prime Factorization Problem

This article introduces a new scientific discovery in the field of computational number theory: an enhanced integer factorization method that unifies an optimized form of a prime generator algorithm with an advanced trial division framework. This integration produces a factorization technique that is both faster and more structurally elegant than conventional approaches. The discovery lies in demonstrating how a modern prime generator can be adapted and expanded to drive the factorization process with greater precision, reducing unnecessary computations and improving overall performance. The paper details the conceptual foundations of the method, outlines its computational advantages, and explains the process choices that make the algorithm both practical and theoretically elegant. The article describes the transformation of a simple prime generator algorithm into a solution for an NP problem, achieving optimized time and space efficiency.