[Siegmund]

As far as algorithm efficiency, yes, quick sort or one of the nearly equivalent O(n log n) methods.

As far as whether the numbers fit into a Long or not... you will want to investigate whether String or Long or user-defined "VeryLong" variants are fastest. You may get faster performance with string comparisons (pad numbers with leading zeros as necessary.)

Ultimately, however, the length of the strings has almost nothing to do with the time needed for the comparison, only with the read and write time for swapping the strings around. The "quick sort" idea of sorting sub-sub-groups and sub-groups first can be adapted to "look at only one bit at a time, and sort into groups based on whether that bit is a 0 or a 1": there is absolutely no reason to compare an entire long string against another entire long string except convenience of programming.