An Interesting Opportunity: The Gilbreath Conjecture

Abstract

Unsolved mathematical conjectures are a rich source of more than just frustration. By looking at the Gilbreath conjecture (unproven since 1878), we explore the learning opportunities that these unsolved problems present. Through explanation of the workings of the conjecture and the previous attempts by mathematicians the reader can develop an understanding of the number theory involved and even get started on a project of their own. This paper provides context for the Gilbreath conjecture so that an entry level mathematician (or person of any study) can get acquainted with an important but relatively unknown portion of mathematics. It also summarizes the work done on the conjecture so that the conjecture can be easily understood using only one source. Intended as both an educational presentation of entry level number theory and as a primer piece for those looking to begin work on the Gilbreath conjecture, this paper will show how rich an opportunity an unsolved conjecture can be.