Remember all those times you took the difference of some value or the remainder of some value from c and a solution value surfaced, but it didn't work for other example c values?
Well, inspired by those lists of values I developed that happen to make x and x+n show up somewhere, I don't think those paths are useless coincedences and should be forgotten, I think we should make a list of them.
I believe that making a list of paths to solution values and numbers they work for and don't work for will lead to a deeper understanding of why those paths worked and what types of semiprimes there are.
And the solution itself.
Just be sure to keep it neat and organized, because searching for solution paths can get out of hand easily (as in organization collapses and you end up with too many numbers to make sense of).
so I looked back at these and realize that sometimes this works even for massive multiples of 5
when gcd(d,e) != 1 it is equal to a
"there is an entire family of numbers that can be factored in 1 step"
which is when x appears in the tree