Mike, here's my answer to the question from the other thread:
I don't know the full scope of the problem, exactly, but it may be valuable to know a few small facts:
Divisible[n,m] checks whether n is divisible by mDivisible[n,{m1,m2,...}] will return a list of divisibility results for all of the m1,m2,...- If you'd like to check multiple numbers at once, it's usually faster to do this via built-in functions' syntax rather than writing your own and then using
Table, Map, or otherwise, so it may be useful to know that you can do Divisible[{n1,n2,...},m] to check the divisibility of all of the n1,n2,... by m.
Select can be used with a list to pick out numbers which meet any given criteria, including divisibility. For example, you could do something like Select[Prime /@ Range[100],
Divisible[660973690464825842286630098265,#] &] to check which of the first 100 primes divide that integer.
Perhaps some of this together is useful, but I'm not sure at all! If you could provide an example, that would be helpful. There are lots of other things to try, like checking the number of digits of all the factors, the number of factors that the number has, and so on, but I don't know what's useful here without a more concrete example.
