Quote:
Originally Posted by storm5510
Having a factor, I don't understand how this could be considered a "firsttime" test. The more I think about all of this, the more my head hurts.

Firsttime test on cofactors after a new factors is found, compared to double checking the same results afterwards (which is not needed anymore if proof files are used).
But PRPCF and PRPCFDC tests are not part of GIMPS main project of finding Mersenne Primes. It is a side project to test if the cofactors are PRP or if there are more factors to be found on those Mersenne numbers, like the side projects ECM on Fermat numbers or ECM on small Mersenne numbers.