We define an abelian loop on a set S consisting of 1 and all odd prime
numbers with an operation β, where for a,bβS, aβb is the smallest element of S strictly larger than β£aβbβ£. We use
theorems and conjectures from number theory to prove properties of the loop and
state analogous conjectures about the loop.Comment: This paper has been accepted for publication in the Missouri Journal
of Mathematical Sciences and is set to appear in 202