Mining with a CPU is long since irrelevant, even GPUs are completely useless as far as mining is concerned. The network uses ASIC hardware now, basically chips designed only to mine Bitcoin quickly and efficiently. Attempting to mine on a CPU is completely futile and does absolutely nothing for the network.
It's not really useless. There is Primecoin that is searching for prime chains as proof of work. At the moment there is no (public?) GPU miner. The involved computations are also difficult to port to the GPU.
Primecoin? It's not solving a "problem" as it claims, there's nothing that can be solved with chains of primes. They're interesting but that's about the end of it. The vastly smaller network means it's a lot more susceptible to attacks.
It's not different from SHA-256 or scrypt in that regard. However there appears to be some interest in these primechains from the scientific community. I never claimed it is solving important "problems" but I like the CPU only property. The Bitcoin GPU/ASIC race favored a few wealthy individuals. 40% of all BTC is in the hands of a few people. I don't see this happen with Primecoin at the moment. GHash.io looks more like a problem for Bitcoin as e.g. botnets for Primecoin.
I'm more interested in better and faster miners for Primecoin as this is a pretty interesting problem to solve. Getting rich with either of these coins is pretty much impossible if you are not already wealthy and able to invest a good amount of money and energy - especially in the BTC ecosystem.
