A Quadratic Cascade Method for Integer Factorization: Empirical Evidence Suggesting a New Algebraic Factorization Channel

Key Points

• The aim is to present a new method for efficiently factorizing integers, particularly semiprimes.
• Introduced the Quadratic Cascade method as an algebraic heuristic for factorization.
• Analyzed performance on 30-digit semiprimes using a 7-formula cascade union.
• Achieved an improvement of 8-9 percentage points over existing methods (Pollard P-1 and Williams P+1).
• Total single-pass coverage for factorization reached approximately 25%.