I'm planning to make a big num library for a project. I want to get some info on good applications of these algorithms and some nice problems which have been solved using this (all this to justify the usefullness of the project). Any help/comment appreciated!

well, are you thinking computing the n-th root of a number? binary search or something... Or gcd... I've seen some interesting algorithms over the net with GCD. Have fun,
PS: implement all C++ operators also (you know...)