Abstract: Aiming at the industry bottlenecks of traditional large integer factorization algorithms (including trial division, sieve methods, GNFS, CADO, etc. ) that always maintain sub-exponential complexity and suffer from explosive computational overhead for ultra-large RSA composite number factorization, this paper constructs a novel Shui’s Prime-Π Duality Axiomatic System (MTSP). It proposes the innovative mechanisms of N-axis topological orbital screening, π³~π⁶ high-dimensional manifold topological mapping, and Π superimposed topological decoupling operation, which completely reconstructs the factor searching paradigm for large integers. Supported by 70 original axiomatic formulas to form a closed-loop system, the proposed method optimizes the traditional one-dimensional global traversal into a brand-new framework of directed orbital sampling + topological curvature prediction + high-dimensional superimposed topological decoupling, breaking the inherent complexity constraints of traditional number theory systems. Theoretical proofs demonstrate that the MTSP system stably achieves a polynomial complexity ofO (² N) for the factorization of semiprime composite numbers, realizing magnitude-level computational superiority over the state-of-the-art GNFS algorithm. It can be efficiently applied to the factorization scenarios of ultra-large RSA numbers ranging from 2048-bit to 16384-bit. Meanwhile, the system is compatible with fundamental number theory problems including prime density analysis, prime gap deduction, and batch prime generation, possessing extremely high theoretical innovation value and engineering practicability.
xiaogang shui (Fri,) studied this question.