In the novel I’m currently working on, which starts 800,000 years in the future, people still don’t know whether all Fermat numbers are square-free, and there is a subplot in which two of the characters devote an astronomically huge amount of resources to see if they can find a proof or a counterexample.
So if anyone wants to punish me for my LLM-scepticism they should try to settle this question before the book is published, forcing me to rewrite it to make that subplot about a different problem.