Optimization applications of Goldbach's conjecture

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

• Goldbach's conjecture
• Design of base components
• Integer programming
• Construction heuristics