AN ABELIAN LOOP FOR NON-COMPOSITE NUMBERS

Abstract

We define an abelian loop on the set $S$ consisting of $1$ and all odd prime numbers with an operation $•$, where for $a,b\in S,a•b$ is the smallest element of $S$ strictly larger than $|a-b|$. We use theorems from number theory to prove several properties of the loop and we use conjectures from number theory to state analogous conjectures about the loop.