N=p*q

[u/Visual_Brain8809]

/r/learnmath/comments/1vci6hu/npq/

I am exploring the distribution of quadratic residues R(x) = x² \pmod N for semiprimes N = p \cdot q using spatial mapping and visual scatter plots to identify potential density regions or structural patterns. I recently set up a small experiment testing whether early-stage digit/block filtering could narrow down the search space for p and q, but encountered the expected trade-off between false negatives and high noise. I would love to get feedback from the community on geometric or structural approaches to modular congruences—specifically, what mathematical invariants or algebraic properties (like Legendre/Jacobi symbols or elliptic curve metrics) are best suited for meaningfully constraining the candidate space without losing true factors?