In my algorithms class, at some point, I teach RSA and primality testing. For the corresponding assignment, I usually have students do a "numerical exercise" which involves, naturally, computing with some big numbers. They also have a later programming assignment where they have to use numbers that may not fit into a standard-programming-language-sized integer. Since this is not a programming class, and I do not prescribe a language for them to use, I essentially tell them it's part of the homework to figure this out.
Surprisingly, it seems to give a number of people significant grief every year. I know that for C and Java it's a pain -- the natural thing to do is to download and install a BigNumber library, which should be easy, but often some trouble arises. (And most students, even though they've had the intro programming courses, do not seem to have learned how to do useful things like download and run useful libraries.) There are other programming languages which handle big numbers essentially transparently -- ah, the days of programming in Lisp -- which are fine for the numerical exercise, but may not be as nice for the larger programming assignment.
My only real point here is that, in those lists of skills I would expect CS majors to have, I'd have to put "being able to do computations with very large numbers" somewhere on the list. Yes, you're unlikely to need it for your standard checkbook program, but it seems to me this issue arises in plenty of places. (It has for me -- and my graduate students -- several times.) And it's not so important that they know how to do this specific task off the top of their head, but more that when they're given a task like this, they are able to find the information they need and complete it in a timely fashion. For better or worse, that's something some of them get out of my class.