Optimization applications of Goldbach's conjecture

Bertrand M T Lin; Shin-Mei Lin; Shyong Jian Shyu

doi:10.1016/j.heliyon.2023.e20550

Optimization applications of Goldbach's conjecture

Heliyon. 2023 Oct 5;9(10):e20550. doi: 10.1016/j.heliyon.2023.e20550. eCollection 2023 Oct.

Authors

Bertrand M T Lin¹, Shin-Mei Lin², Shyong Jian Shyu³

Affiliations

¹ National Yang Ming Chiao Tung University, Institute of Information Management, Hsinchu 300, Taiwan.
² Stella Matutina Girls' High School, Taichung 404, Taiwan.
³ Department of Computer Science and Information Engineering, Ming Chuan University, Taoyuan 333, Taiwan.

Abstract

Goldbach's conjecture is an unsolved legendary problem. In this paper, we investigate an optimization problem as an attempt to discuss potential applications of the conjecture. In an optimization perspective, the research question, modelled from design of base components, is to select a minimum number of primes to span a given set of target even integers. We formally define the problem, propose integer programming formulations, and develop solution procedures, which are then tested through a computational study.

Keywords: 11A99; 65K10; 90C27; Construction heuristics; Design of base components; Goldbach's conjecture; Integer programming.