World's most painful compression algorithm: Finds a mathematical series of infinite digits, and the offset into it, that most efficiently compresses data passed in. Probably have to chunk the data up to make this efficient.

Of course one can argue that all current real life compression algorithms are aiming to simulate this, and that a brute force algorithm is one of those "after turning the sun into a CPU, still won't have enough compute power to finish the problem" types of solutions.