This paper develops a structural framework for prime numbers based on covering irreducibility and loop representations. Multiplicative structures are interpreted as factorized configurations with intermediate coverings, while additive structures correspond to independent loop compositions. Within this framework, even numbers naturally exhibit a two-loop structure, and the Goldbach problem is reformulated as the question of whether this structure can be realized by two prime loops. The approach provides a geometric intuition for the conjecture without claiming a proof.
Jeong Min Yeon (Sat,) studied this question.