What question did this study set out to answer?

The aim is to classify the prime factor residues of semiprimes modulo 90 in a size-independent manner.

February 5, 2026Open Access

A Fixed Modular Classification of Factor Residues for Semiprimes Modulo 90

Key Points

The aim is to classify the prime factor residues of semiprimes modulo 90 in a size-independent manner.
Developed a closed multiplicative structure for residue classification
Identified 24 admissible residue pairs for corresponding factors
Focused on structural and classificatory contributions without algorithm development
Established a complete classification of residues for semiprimes modulo 90
Demonstrated that each semiprime corresponds to exactly one of the admissible residue pairs
Clarified that the work does not reduce the complexity of factorization

Abstract

This preprint presents a complete and size-independent modular classification of the residues of the prime factors of semiprimes modulo 90. The construction relies on a closed multiplicative structure that guarantees that, for any semiprime N, exactly one of 24 admissible residue pairs corresponds to the true factor residues. The contribution is structural and classificatory rather than algorithmic and does not claim a reduction in the asymptotic complexity of factorization.

A Fixed Modular Classification of Factor Residues for Semiprimes Modulo 90

Key Points

Abstract

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