Challenges like this are a little difficult to judge because they're effectively asking us to write a program that solves an unsolved mathematical problem. Until such a time as there is verified proof of a solution to the underlying mathematical problems, we cannot know for certain what the upper limits of these programs need to be or what their output should be once that limit is reached.
Most currently unsolved mathematical problems cannot be simply solved by brute force - if they could, people with larger brains, more money, and bigger computers would probably have cracked them by now. So, essentially these are impossible questions. Sure, we can validate that the program is written in a way that it should produce the expected output. But until we know for certain what the answer to the underlying mathematical problem is, we have no way of authoritatively testing this.
Should questions like these be allowed? What should be some guidelines for posting and judging them?