The largest I've seen [1] is an exponent of 10^12, which I suppose still counts as polynomial time.
I'm sure all of these super small or large constants will improve over time, but it's still amusing. It is entertaining to see the exponents directly rather than have them hidden as n^c or epsilon or O(1).
[1]: https://github.com/openai/math/blob/main/preprints/Determini...