This paper proposes the Prime Space Cluster Hypothesis, which deeply couples the number-theoretic properties of prime numbers with the topological structure of cosmic spacetime and the fundamental laws of symmetry conservation. It reveals that primes are not isolated number-theoretic entities but topological cluster markers of high-dimensional space manifested in three-dimensional physical spacetime. The distribution law, coprimality, and twin prime pairs of primes correspond to the dynamic processes of symmetry breaking and conservation restoration in the universe, and the topological dimension of prime clusters is isomorphic to the coupling dimension of cosmic fundamental interactions. This study establishes the qualitative correspondence between prime space clusters and cosmic symmetry conservation, derives the basic topological conservation equation of prime clusters, and explains the ontological origin of the coexistence of large-scale uniformity and small-scale inhomogeneity in cosmic spacetime. Based on number-theoretic derivation and topological analysis, combined with cosmological observational facts, a theoretical framework of prime space with the unity of mathematics and physics is constructed, and three testable theoretical predictions are proposed for the statistical characteristics of dark matter/ dark energy distribution, the energy-scale dependence of fundamental interaction coupling strengths, and the distribution of high-dimensional structural prime pairs. As an exploratory theoretical hypothesis, it provides a new interdisciplinary research path for the integration of number theory, cosmology and high-energy physics, and is published in open access for academic discussion and verification.
Jian Wen (Tue,) studied this question.