Prime Strictly Concentric Magic Squares of Odd Order

Abstract

Magic squares have been widely studied, with publications of mathematical interest dating back over 100 years. Most studies construct and analyse specific subsets of magic squares, with some exploring links to puzzles, number theory, and graph theory. The subset of magic squares this paper focuses on are those termed prime strictly concentric magic squares (PSCMS), and their general definitions, examples, and important properties are also presented. Previously, only the minimum centre cell values of PSCMS of odd order 5 to 19 were presented, by Makarova in 2015. In this paper, the corresponding list of primes for all minimum PSCMS of order 5 is given, and the number of minimum PSCMS of order 5 is enumerated.

Keywords

• magic squares
• prime
• concentric
• enumeration