There are some very large and fast computers in the world.
Problem is, they are also very expensive to operate.
Just get a few hundred of your friends together to help you. Create a software program that only uses the spare time in a computer to run computations. Divide your mathematical dilemma into pieces and let all of those home computers work on them at the same time. Chances are, you'll have the answer you're looking for quicker than if you had actually used one of those supercomputers. This technique is called distributed processing and is gaining in popularity.