Infinitely many loops in the Euclid-Mullin graph

Let $G_1$ be the Euclid–Mullin graph associated with the initial node $1$, whose edges and loops are defined by the graph construction in the paper. Infinitely many loops conjecture. The graph $G_1$ contains infinitely many loops. This is motivated by a heuristic that nodes on the right-most branch become equidistributed among invertible residue classes modulo a fixed modulus; the conjecture remains open.