If this is the case, how would I go about using it?
Another thing I noticed in the Miller-Rabin test is the list of primes needed to check against for a set of number.
Which makes me think of q. Which also makes me think vqc =vector q, c? That we make a list of primes from column 1 (q) which we then use in a modification of the Miller-Rabin test against c to determine if it is a prime or not (and to get a factor).
Since the Miller-Rabin constructs a tree (although not directly, but abstractly) we'll do the same, but the end result will be similar. In the end we won't need to construct the tree, but for now it is a helpful method of learning. How far off am I? I can easily be way, way off.