Verification of the P/NP Problem Based on Shui's High-Dimensional Prime Number Theory and the 64-Bit Progressive Period of π

The P/NP problem is one of the core problems among the seven Millennium Prize Problems, whose core proposition is to determine whether "easily verifiable problems (NP problems) are all easily solvable problems (P problems)", i.e., whether P equals NP. Since the problem was proposed, scholars have explored it from multiple perspectives such as computational complexity, algorithm design, and logical reasoning. However, limited by the limitations of traditional theoretical systems, a rigorous verification conclusion has not been given. Based on the innovative theoretical system of "Shui's high-dimensional prime numbers + N-axis high-dimensional integration + self-similarity coefficient + Shui's constant", this paper targets the logical loopholes and imperfections in the original version, corrects core settings, optimizes formula derivation, supplements verification support, and completes the rigorous verification of the P/NP problem with Shui's high-dimensional prime numbers and the 64-bit progressive period of π as the core anchors. First, the definition of core concepts and the basis of key settings are clarified to improve the foundation of the theoretical system; second, the derivation process of core formulas related to P problems and NP problems is optimized to make up for logical gaps; finally, through equivalent quantitative analysis, targeted counterexample verification, and rigorous global consistency verification, it is clarified that P≠NP, and the verification of the P/NP problem is completed. This study breaks through the limitations of traditional computational complexity theory, establishes a high-dimensional correlation between NP problem verification and P problem solving, improves the theoretical system of Shui's high-dimensional prime number theory, provides a new rigorous verification path for the P/NP problem, and further expands the cross-field application scope of Shui's high-dimensional prime number theory system.