Comment by Gro-Tsen on Is there a statement in Presburger arithmetic about primes this simple heuristic fails for?

I have a meta-question, which is whether the second paragraph in the conjecture's statement is algorithmically decidable (i.e., whether given $s$ we can algorithmically decide whether for all $M$ the probability (…) is $1$). Maybe this should be made into a separate question.