2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94782An algorithm is given to factor an integer with $N$ digits in $\ln^m N$ steps, with $m$ approximately 4 or 5. Textbook quadratic sieve methods are exponentially slower. An improvement with the aid of an a particular function would provide a further exponential speedup.8 pages, LaTeX, v1: correction to a_{C_N}\neq 1 and improved analysis to general case, v2: added addendum paper to original analysisGeneral Physicstext