Kernel Factor Pairs for Semiprime Factorization

We show that any semiprime number can be factorized as the product of two prime numbers in the form of a kernel factor pair of two out of 48 root numbers. Specifically, each natural number without factors of 2, 3, 5 and 7 can be traced back to one unique number of a total of 48 root numbers falling in [ 11, 220 ] in periods of length 210. Unlike the commonly used sieve-based methods, under no preconditions, will the proposed kernel-factor-pair-based algorithm be guaranteed to successfully factorize any given semiprime α by searching over 1/2 logα binary variables. The proposed method is well structured for factorization in breaking RSA encryption and is readily applicable for parallel computation.