Number Theory

    

Modular Symmetry in Goldbach Partitions: A Dual-Channel Combinatorial Analysis

Authors: Chenglian Liu, Sonia Chien-I Chen, Ruopengyu Xu

This paper establishes a rigorous connection between modular arithmetic constraints and enhanced Goldbach partition counts through dual-channel prime pair combinations. We demonstrate that even numbers $ x equiv 0 pmod{6} $ exhibit $3.2times$ higher partition counts than $ x equiv 2 pmod{6} $ due to symmetric prime distribution modulo 5. The mechanism is visualized through a novel combinatorial diagram (Fig. 1) and supported by statistical analysis ($ x leq 10^4 $).

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[v1] 2025-04-20 06:57:07

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