Feynman on Fermat's Last Theorem (2016) (lbatalha.com)

I think it would be fun to construct a similar conjecture where the same kind of probabilistic analysis says that it's very likely to be true but it is in fact false.

Previous discussion: https://news.ycombinator.com/item?id=12018221

How can he integrate the probability expression rather than do a summation? Surely there are many real values of x and y that lead to perfect powers? Yet the probability tends rapidly to zero.