I'm an active and more acknowledged member of the project. To explain and correct things: There are two types of primality checking algorithms for Mersenne nu

I'm an active and more acknowledged member of the project. To explain and correct things: There are two types of primality checking algorithms for Mersenne numbers, PRP (probable-prime test) and LL (Lucas-Lehmer test). PRP does only say that the number is most probably prime, whereas LL, if correctly computed, says it with 100% certainty (i.e. it definitely is or definitely is not a prime). PRP tests have better error correction algorithms, and new feature is "Certification", which is rather complicated, but basically, it can confirm, that PRP was done correctly, but if the PRP indicates that number is prime, LL must be still done to be sure. LL test can have a lot more error, that are unnoticed by the existing error correction (which is different from the one used for PRP), thus it has to be at least DOUBLE-checked, not triple-checked. Triple checks are only necessary if the previous two runs don't match. If not even third run matches, fourth one is run, etc. The order of assigning tasks is not uniform at all, there are "Categories" of assignments. Simply said, the more assignments computer finishes and turns in, the lower numbers it can get assigned next. If it returns a result, that turns out to be bad, it is downgraded in the eyes of the server, meaning it kind of goes back to the higher exponents. This is done so that the "wavefront" moves as quickly as possible with current amount of computing power. I will probably write more later. Until then, you all can explore the page, especially the "More Information / Help" tab.