The Prime95 software will normally stop when it finds a factor.
There is an secondary effort that PrimeNet coordinates that look for more factors for the lowest nonprimes. There are attempts to fully factor the smallest of the numbers. There are a few individuals that are working on getting every factor found at each bit level, as well.
Part of the effort to fully factor all of the lowest number is doing a PRP test on the remaining 'cofactor'. If it shows that the cofactor is composite, then there will be efforts to find more factors.
General order TF, then P1, then ECM, then if there are more factors yet to be found, "bigger guns" may be brought to bear.
