2-Adic Semiprime Factorization - The Lewis Sieve
2-Adic Semiprime Factorization 2-Adic Semiprime Factorization Geometric Structure, Complete Algorithm, and Complexity Analysis April 2026 Abstract This paper presents a complete geometric analysis of a 2-adic candidate sieve for factoring semiprimes of the form $N = p \times q$, derived entirely from the structural patterns observed in the divisibility ladder (detailed in the appendices). The core contribution is the identification and proof of the $v_2(S) = 2$ Theorem : that for any semiprime $N = p \times q$ (where $p, q$ are odd primes), both prime factors appear at rows in the sequence $S = 4p$ and $S = 4q$, each exhibiting a unique three-level divisibility signature — one non-trivial integer mod, followed immediately by a zero mod (the factor), followed by a decimal-valued divisor. We prove that all such rows lie strictly be...