A Computational Exploration of Spectral Regularities in Prime Number Sequences

Abstract This work presents a computational and structural investigation into spectral patterns emerging in the distribution of prime numbers. Rather than proposing a proof of classical conjectures, the study focuses on identifying regularities, resonances, and geometric structures that arise from large-scale numerical exploration. By treating prime sequences as dynamic systems, the paper analyzes their behavior through spectral visualization, transformation mappings, and pattern detection. The results suggest the presence of non-trivial structural features that can be interpreted in terms of emergent order within apparent numerical irregularity. The approach is intentionally exploratory and interdisciplinary, bridging computational mathematics, complex systems theory, and structural analysis. The goal is not to replace existing analytic frameworks, but to provide an alternative phenomenological perspective on prime number behavior, emphasizing structure over proof. This study aims to stimulate dialogue between mathematics, physics-inspired modeling, and complexity science, proposing a framework in which prime numbers can be examined as objects of structural dynamics rather than solely as elements of formal number theory. Description This paper presents an exploratory computational study on structural patterns emerging in prime number sequences. Through large-scale numerical analysis and spectral visualization techniques, the work investigates whether apparent randomness in prime distribution conceals deeper geometric or dynamical regularities. The study does not attempt to provide formal proofs of classical conjectures. Instead, it offers a phenomenological and structural perspective, treating prime numbers as objects of dynamic organization. The goal is to stimulate interdisciplinary dialogue between number theory, computational mathematics, and complex systems research. The work is intended as an open exploratory contribution and an invitation to further analysis, critique, and extension.