Death: I'm probably not the person to be answering those questions, but I'll give it a shot. There are shortcuts for sierpinski and riesel numbers (those forms that you suggested). Unfortunately, there doesn't seem to be such shortcuts for other forms.

There are some more details at the coordinating forum: http://www.mersenneforum.org/forumdisplay.php?f=86

Phil Moore wrote a good introduction to the project. The Integers paper (linked in the SoB forum here at Free-DC, the main SoB site, and the mersenneforum linked above) had some more technical details if you're interested.