ADVANCED OPTIMIZATION OF PRIME FACTORIZATION

The manuscript treats prime factorization as an algorithm-engineering problem while preserving the mathematical foundations required for correctness. The central comparison is deliberately narrow: an integer-candidate trial-division factorization baseline versus a prime-candidate factorization framework. More advanced factorization algorithms are introduced later only to establish the limits of the proposed approach and to define a meaningful future comparison program. This scope keeps the scientific narrative coherent and prevents unrelated algorithm families from obscuring the measured contribution.