Alan Verdegraal, Mountainair, USA

In Mathematics, for any Natural Number n, there is no general procedure to determine whether n-1 or n+1 is a prime or composite simply by examining n itself. Factorization of n fails to produce meaningful information regarding the primality of n-1 and n+1. The research being discussed in this paper shows how representing a number n as a distinct set of sequences, heuristically derived from a circle with n points, demonstrates the primality of not only n but of n-1 and n+1; i.e., the Natural Number n "knows" whether its immediate neighbors n-1 and n+1 are either prime or composite. This method, although simple to comprehend, has significant implications for the Theory of Numbers

Number Theory, Primality Checks, Prime Numbers, Composite Numbers