Fouad's Algorithm: Deterministic Factorization for RSA-2048

"URGENT CORRECTION NOTICE (January 2, 2026): Please be advised that the 2048-bit RSA Key (617 Digits) currently provided in the uploaded file/description contains a typographical error. This specific numerical value is being verified and will be updated to the correct version within the next few hours. Consequently, the calculated search range (Start/End Bounds) based on this specific key should be reconsidered until the corrected value is published. We apologize for this oversight."