A good source for highly efficient algorithms and implementations for this kind of problems is [Dan Bernstein's homepage](http://cr.yp.to/djb.html). [There](http://cr.yp.to/smallfactors.html) I found an algorithms that might be useful for weeding out all the small prime factors: 

If you have $y/(\log y)^{O(1)}\;$ integers, each with at most $(\log y)^{O(1)}\;$ bits, then you can find all the small prime factors of each integer in time $(\log y)^{O(1)}\;$ per integer.

[I didn't look at the details, so you will have to give it a try to see if 60-bit numbers are already big enough.]