TITLE:
Kernel Factor Pairs for Semiprime Factorization
AUTHORS:
Han-Lin Li, Shu-Cherng Fang, Way Kuo, Nianrui Lin
KEYWORDS:
Semiprimes, Factorization, Factor-Pairs Table
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.15 No.9,
September
22,
2025
ABSTRACT: 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.