Fouad's Algorithm: Quantitative Search-Space Reduction for Large Composite Numbers (Including RSA-768)

Fouad’s Algorithm introduces a high-precision method for analyzing extremely large composite numbers by drastically reducing the numerical search space around their prime factors. This repository presents quantitative results demonstrating how the algorithm narrows the search corridor, enabling efficient factorization of numbers ranging from 20-digit composites to the 232-digit RSA-768 key. The key contributions include: Demonstrated search-space reduction for multiple large numbers, showing reductions from the total numerical domain to less than one-billionth of the original space. Efficient extraction of prime factors with minimal computational steps, highlighting the algorithm's potential for optimizing classical and future quantum computing approaches. Quantitative analysis showing proximity of approximated factor values to the actual prime, emphasizing deterministic and predictable localization without disclosing internal secret operations. This work provides a proof-of-concept for numerical search-space optimization, which could significantly influence large-number factorization and cryptographic research. It is intended for researchers, cybersecurity experts, and technology companies interested in exploring advanced computational techniques for analyzing high-complexity numerical systems. Strategic Inquiry:Could the drastic reduction of search space achieved by Fouad’s Algorithm enable current or near-future computing systems to factor real-world RSA keys more efficiently?