Number Theory

    

Modular Patterns in Semiprimes: Empirical Observations and Conjecture on Factor Sums and Deterministic Congruence Patterns in Semiprimes Enabling Optimised Factorization

Authors: Chandhru Srinivasan

I report an empirical derived and theoretically motivated analysis of modular patterns in composite integers, with a focus on semiprimes. For any odd semiprime N(possibly all N ∈ ℤ), the results indicate the existence of N-1congruences of the form p+q≡r(modm), where p and q are factors of N, m∈{2,u2026,N-1} as 1 and N are trivial and always N ≡0 mod(1 or N) , and each residue r belongs to a restricted, well-structured subset R_m. Empirical experiments suggest that these residue constraints are non-random, deterministic and encodes all the necessary information about the factor pair (p,q). I formalize this observation as a conjecture and provide preliminary reasoning for its generality. These results point toward a potentially deterministic structure in the modular representation of factor sums, and potentially speedup the factorisation of any N and offering a new perspective on the arithmetic properties of semiprimes and composite numbers. I invite further mathematical verification and formalization.

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[v1] 2025-10-13 20:19:05

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