Hi, could you please give us an example of such a conjecture ?

Dear Samir, I think there is not a "best" statistical approach to check a mathematical conjecture; if the conjecture is true, you can work for about 10^10...0 tests/experiments with positive results but you have not mathematically proven the conjecture; if it is false, you can work for about 10^10...0 tests/experiments with positive results but the (10^10...0 + 1)th test (which for some reason you have not tested) is negative. See histories about some past conjecture (Fermat Last Theorem, Poincaré, Goldbach). Gianluca

Yeah, this tool can help falsifying a claim, but never verify that the claim is true.