Although any theorem (or true conjecture) can be computationally checked, many long-standing open problems have been computational verified for very large values. For example, the Collatz Conjecture and Fermat's Last Theorem (before it was proven) were computationally verified by large scale computation programs. Not only have these calculations been carried out, but there is a lengthy history of improving the bound for which these calculations have been carried out until.
What are other problems (not necessarily from number theory) have been similarly verified for values up to some large bound, and how high have they been checked? Specifically I’m interested in cases where is an established history of computationally verifying the problem up to larger and larger bounds.
I’m interested both in the current cutting edge and the history of the computation.