Simple proof of work example? Can anyone show me a simple proof of work algorithm that I can use to stop spammers? I've looked at hashcat, but i think there's a bit too much specialized hardware for bitcoin mining. 

That is, the time required to calculate one proof of work on a mobile device cpu is way too long compared to a bitcoin mining rig using asic-miners.
Bitcoin ASIC miners are specialized hardware, which is capable of computing SHA-256 only. If you change almost any parameter in the Bitcoin proof-of-work, the existing miners will be useless. For instance, you could just change SHA-256 to SHA-1 or SHA-3.

To be more efficient against spammers equipped with GPU, you might want to employ a hash function that requires a certain amount of memory to compute hash. Scrypt is a reasonable choice with hundreds MBytes of RAM as a parameter, and the ongoing Password Hashing Competition will likely to produce better and faster candidates.