I agree that the observation "M_1(n) = n+1 iff n is prime" is elementary. It certainly motivates some intuition behind the investigation in this paper, but I'd

I agree that the observation "M_1(n) = n+1 iff n is prime" is elementary. It certainly motivates some intuition behind the investigation in this paper, but I'd loathe to call it obvious. Note that the paper studies equations with polynomial coefficients on McMahon series. That is, the n+1 in our trivial observation is "stray" in a sense. For an at-a-glance indication of nontriviality, look no further than the conjecture associated with Theorem 1.2 -- that there are exactly five equations of this sort which are prime indicators. That seems spooky, to me; I can't help but wonder what structure underlies such a small number of relations.