What traits make a number a good choice for NFSNET? Is the size of the base number (227 digits for 10^2271) important? Is ths size of the composite cofactor (212 digits for 10^2271) important? How big is "too big to be interesting?" How much previous work should have been done by other methods?
Several characteristics are taken into account. Perhaps the most important is that it should not be too hard (or we'd never get it finished with the resources we have) or too easy (or we'd spend more time on administration than computation. For SNFS, the range is about 180 to 240 digits. For GNFS the range is perhaps 135 digits to 165 digits.
For the time being we want to do numbers which are of some mathematical interest, which means in practice they come from a number of well know tables of factorizations associated with various projects. Almost all so far have come from the Cunningham project.
We don't want to spend a great deal of effort finding a factor which could have been found much more easily with the Elliptic Curve Method, so we generally require that a NFSNET candidate have had enough ECM work done on it that it's unlikely to have a factor below 50 digits or so.
Paul
