This work presents a deterministic approach to the factorization of RSA semiprimes restricted to the congruence class N≡7 (mod180) N 7 180 N≡7 (mod180). By exploiting the rigid modular structure induced by this condition, the search space of Fermat’s difference-of-squares method is reorganized into 24 congruence lanes. The framework combines structured initialization, bidimensional pruning using vertical columns Nmin (k), Nmax (k) N_ (k), N_ (k) Nmin (k), Nmax (k), horizontal index jumps, and local refinement via quadratic synchronization (Gap C). All operations are performed in the integer domain to avoid precision issues with large numbers. The method is offered as a contribution to the exploration of structured factorization techniques. This manuscript was prepared by the author as a personal hobby project. Grok AI (developed by xAI) was used solely for language polishing, formatting, and improving clarity. All mathematical ideas, analysis, and final decisions are entirely the author's own.
Gisela Bühl (Fri,) studied this question.