A Proposal for Structured Semiprime Representation Using Arithmetic Progressions and Factorization Implications (revised)

Key Points

• The aim is to present a structured method for representing semiprimes using arithmetic progressions and their factorization implications.
• Developed representations of semiprimes as differences of squares from modular classification.
• Utilized known parameters a₀, b₀, and k to reduce factorization to a one-dimensional search.
• Implemented a bound range Δ around a candidate index i_cand for efficient searching.
• Applied step k and parity filtering to condense the search space.
• Demonstrated a significant reduction in search space for factorization of semiprimes.
• Illustrated the implications of structured representations on security limits.