An Optimization Energy Flow Framework for the Goldbach Conjecture: Prime Potential Functions and Energy Minimization Dynamics

Goldbach's Conjecture is one of the most important unsolved problems in analytic number theory, asserting that any even number greater than 2 can be expressed as the sum of two prime numbers. Traditional research methods mainly include the circle method, the sieve method, and the theory of prime number distribution. This paper proposes a new research framework that transforms Goldbach's Conjecture into an optimization theory problem. The core idea is to construct a new prime potential function and thereby establish a completely new Goldbach energy equation. This equation transforms the integer factorization structure into an energy minimization problem, thus interpreting prime pairs as stable minimum states of the energy function. This paper systematically establishes the mathematical structure of this optimization model, proves the correspondence between the energy function and the prime number structure, and proposes a new optimization dynamic system for searching prime factorization. This framework provides a new geometric-optimization perspective for studying Goldbach's Conjecture and lays a theoretical foundation for future research on number theory problems using optimization theory.