Author(s)

Han-Lin Li¹, Shu-Cherng Fang², Way Kuo³, Nianrui Lin⁴

¹Department of Computer Science, City University of Hong Kong, Hong Kong, China.
²Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, USA.
³Hong Kong Institute for Advanced Study and Department of Data Science, City University of Hong Kong, Hong Kong, China.
⁴Department of Systems Engineering, City University of Hong Kong, Hong Kong, China.

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 $\left[11,220\right]$ 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 $\alpha$ by searching over $1/2\log \alpha$ binary variables. The proposed method is well structured for factorization in breaking RSA encryption and is readily applicable for parallel computation.

Semiprimes, Factorization, Factor-Pairs Table

Li, H.-L., Fang, S.-C., Kuo, W. and Lin, N.R. (2025) Kernel Factor Pairs for Semiprime Factorization. Advances in Pure Mathematics, 15, 629-642. doi: 10.4236/apm.2025.159032.