Is pure mathematics more a game than a utility?

Having read Fermat's Last Theorem by Simon Singh, an account of how mathematician Andrew Wiles over a period of 40 years solved the riddle of ; x^n + y^n = z^n .... for no whole numbers >2, it makes me wonder at the usefulness of this solution. Don't get me wrong, the book is one of the best I've read, and I think Wiles is a brilliant mathematician. My question is more about the role of pure mathematics and how it relates to the world in general. For instance, much effort has been devoted to finding a formula for pin pointing prime numbers, yet I've heard of only one application for prime numbers, and if such a formula is found, it would render that one application in cryptography useless. I'm just a non-mathematician seeking enlightenment.