[Extigy]

It can happen, the Pólya conjecture is the usual example which holds until n = 906150257.

Another fun one I just found is the statement “n^17 + 9 and (n + 1)^17 + 9 are relatively prime”. The first counterexample is at n=8424432925592889329288197322308900672459420460792433.

[dilippkumar]

How does one even find something like this? Let alone prove that this is the first counterexample. That number looks to be in the order of the age of the universe in millionths of a quectosecond!!