Programming Logic: Finding the smallest equation to a large number

Question

I do not know a whole lot about math, so I don\'t know how to begin to google what I am looking for, so I rely on the intelligence of experts to help me understand what I am

Answer 1

I asked the question "what's the point of doing this", as I don't know if you're looking at this question from a mathemetics point of view, or a large number factoring point of view.

As other answers have considered the factoring point of view, I'll look at the maths angle. In particular, the problem you are describing is a compressibility problem. This is where you have a number, and want to describe it in the smallest algorithm. Highly random numbers have very poor compressibility, as to describe them you either have to write out all of the digits, or describe a deterministic algorithm which is only slightly smaller than the number itself.

There is currently no general mathemetical theorem which can determine if a representation of a number is the smallest possible for that number (although a lower bound can be discovered by understanding shannon's information theory). (I said general theorem, as special cases do exist).

As you said you don't know a whole lot of math, this is perhaps not a useful answer for you...