Finding a point in an infinite space

[Caerulea]

Since we're limited to whole numbers, how efficient would be asking for divisibility? Is it divisible by 2 / 3/ 4... Skipping obviously wrong questions. (which is mostly just a way to get the binary approach to normal numbers) Is it much worse than other techniques?

I think prime numbers would be best if you are looking at factors. Maybe something like:

1. Is the number divisible by prime p?
2. If Yes: store p and ask about two again, If no:
3. Is the next prime large than the number? If so: break. (There is probably a smaller end condition that could be used).
4. Is the number divisible by the next prime? Goto step 2

It takes iterations equal to amount of the number's prime factors + the number of primes less than the number that are not prime factors.

—Caerulea