The N-axis studied in this paper is a new mathematical carrier derived from the specific factorization law of prime numbers. Its core construction logic (key content) is: all prime numbers can be factorized by the formula P = 2ⁿ + k (where k \3, 5, 7\, n N, and N is the set of non-negative integers). The continuous distribution of n-values corresponding to prime numbers forms an irregular fluctuation curve n (P) ; performing 11-dimensional or 64-dimensional 11th-order differentiation on this curve can eliminate fluctuations and straighten it into an N-axis with stable laws. The core characteristic (key content) of the N-axis is that different positions on it correspond to different mathematical and physical structures, and the rotation of the N-axis and the mutual interference of multiple N-axes can produce rich connotation extensions. This characteristic endows it with unexpected advantages in explaining the origin of life and spacetime structure. As a core transcendental number running through geometry, algebra, and number theory, π has a profound intrinsic relationship (key content) with this N-axis: the stable law of the N-axis provides a new carrier for the study of the number-theoretic properties of π, while the invariance of π provides the underlying support for the differentiation measurement, law verification, and structural interpretation of the N-axis. Through prime factorization formulas, high-dimensional differentiation formulas, and derivation processes, this paper systematically analyzes the construction logic of the N-axis and its correlation mechanism with π, focuses (key content) on establishing a direct connection between prime numbers and π through formula derivation, demonstrates that the N-axis theory inherently contains the core connotation of the Riemann Hypothesis, expands the application interpretation of the N-axis in fields such as the origin of life, spacetime structure, cryptography, and artificial intelligence, deeply explores its multiple values, and provides a new idea (innovative content) for the exploration of prime number laws and interdisciplinary research. The innovations and breakthroughs (innovative content, breakthrough content) of this paper lie in: constructing a complete theoretical system of the N-axis derived from prime factorization (innovation + breakthrough), establishing a direct formulaic connection between prime numbers, the N-axis, and π (innovation + breakthrough), realizing the organic integration of number theory, high-dimensional mathematics, and interdisciplinary applications (innovation + breakthrough), breaking the limitation that traditional prime number research and π research are isolated from each other (breakthrough content), and proposing a new path for verifying the Riemann Hypothesis and a new method for interdisciplinary applications based on the N-axis (innovation + breakthrough) ; among them, the paradigm content is: the research paradigm centered on "prime factorization → high-dimensional differentiation to construct the N-axis → correlation between the N-axis and π/Riemann Hypothesis/topology/Kähler-Einstein space → interdisciplinary application landing", providing a standardized framework for similar interdisciplinary mathematical research, specifically covering the four-layer research paradigm of "formula derivation → logical verification → case support → application expansion", and the standardized application paradigm of the N-axis in high-dimensional modeling, fluctuation elimination, and law quantification.
Xiaogang shui (Tue,) studied this question.