Analysis of Multiplication Tables by Sum, Difference and Product: A New Approach to Primality

This paper systematically studies the properties of multiplication tables through three fundamental operations: ΣT , ΔT , ΠT . We show how these opera- tions reveal deep arithmetic structures, leading to an innovative primality test. A logarithmic version optimizes computations for very large numbers. Applica- tions are proposed in algorithmic and mathematics education.