The trouble with "a string of unique numbers" is generating them so they are not repeated - random numbers don't guarantee that (in my experience they seem to positively guarantee that they do repeat...)
There is a solution though: GUIDs.
Have a look at this:
PHP: com_create_guid - Manual[
^] it generates a string that is very unlikely to repeat at all. I use them for file storage, with a DB entry which converts them back to file name and the user that uploaded it, allowing for multiple users with the same file name but different content.