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