A Dataset and A Dynamic Distributed Parallel Network for Identifying Divisors of Odd Composite Integers
Hao Li
Guangzhou College of Applied Science and Technology, Guangzhou City, 511370, PRC, China.
Zhiying Liu
Guangzhou College of Applied Science and Technology, Guangzhou City, 511370, PRC, China.
Xingbo Wang *
Guangzhou College of Applied Science and Technology, Guangzhou City, 511370, PRC, China and Foshan University, Foshan City, 528000, PRC, China.
*Author to whom correspondence should be addressed.
Abstract
For a given odd integer N = pq , where p and q are prime factors satisfying 2 < p < q, we define a dataset that systematically accumulates multiples of p and q. This dataset is isomorphic to a rectangular lattice structure described in terms of rows and columns. We then design a dynamic distributed parallel network to search for a multiple of p or q, enabling the calculation of a divisor of N via the greatest common divisor (GCD) between the identified multiple and N. Experimental results demonstrate that the defined dataset provides a novel scenario for applying search algorithms to identify divisors of N and the designed dynamic distributed parallel network operates efficiently when paired with an appropriate search method.
Keywords: Integer factorization, distributed parallel computing, randomized algorithm, lattice