Running this now. I like how they have a big "Number of counterexamples found: 0" in the UI. Imagine they would find a counterexample on your machine… From time to time I switch to the tab to make sure the zero is still a zero (I guess there is basically no chance, but who knows?)
Haha, finding even a single counterexample would be a nightmare.
Surely, finding a counterexample would be huge news, a noteworthy advance in mathematics, and thus a great and widely praised achievement.
It'd also be an end to the project and would make the conjecture far less interesting.
IMO it would make the conjecture far more interesting, as it would be a surprise to most people who have thought about the problem.
Many natural questions would arise, starting with “Is this the only counterexample?”
Possibly, but it would join other false conjectures such as Euler's sum of powers conjecture - posed in 1769 and no counterexample found until 1966. There's only been three primitive counterexamples found so far.
(I got that from https://math.stackexchange.com/questions/514/conjectures-tha... which features some other false conjectures that may be of interest to you)