A good source for highly efficient algorithms and implementations for this kind of problems is Dan Bernstein's homepage. There 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.]