I am a long time Boinc-er (using the Berkley distributed computing platform) and between the projects I participate, there is one called PrimeGrid and it is all about various prime number mathematical work, one of them is finding various kind of them.
The projects uses GPU in some of their calculation, so maybe it could interesting to look at what they are using it for and get some new ideas.
As far as I am aware there are a few Primecoin GPU mining code bases to use:
Claymore and PrimeGPU