Abstract: Traditional number theory generally adopts the simplified assumption of equal-weight and homogeneous primes. Although effective for macroscopic statistical analysis, this paradigm fails to explain refined characteristics of prime distribution, local numerical fluctuation and spectral evolution. Consequently, core problems including the symmetry of Riemann zeta zeros, twin-prime distribution, structural features of π, and high-efficiency large-integer factorization lack a unified geometric interpretation framework. This paper proposes a self-consistent double-layer topological model for primes. Based on structural contribution differences in integer modular spaces, primes are classified into inner primitive structural primes and outer high-order harmonic primes. Relying on low-level primitive primes, three hierarchical periodic bases (30, 210, 30030) are constructed, forming a dual-layer topological analysis framework together with phase-spectrum decomposition methods. The model suggests that small inner primes dominate the fundamental modular structure and symmetry of natural number spaces, while large outer primes mainly introduce local spectral perturbations without altering the global topological framework. This framework provides new geometric interpretations for prime orbital constraints, zeta zero symmetry, twin-prime aggregation and hierarchical characteristics of π. Meanwhile, structural stratification effectively optimizes traditional traversal algorithms and improves the efficiency of large-integer primality testing and factorization. As a supplementary, explanatory and verifiable geometric number theory framework, the proposed model enriches structural analysis tools for discrete number theory and complements empirical paradigms in classical arithmetic research.
xiaogang shui (Sat,) studied this question.