Oh, I see. Yeah, I supposed it should do something like this, given that the operation couldn’t be affected itself without altering it. Only to further detail this thing to anyone interested, I’ll post here the complete formula now that I know what the Factor does:
1 - (1 - c1)(1 - c2 * f)
Where f is the Factor.
Thanks for the answer, doubt clarified! 
EDIT: I return here a time after setting my question as answered just to prove my formula.
As we can see in the Blender source code, the formula for the screen blend mode is not what I wrote… or is it?
Turns out it is.
There, we find the formula (adapting it to more readable terms):
1 - (1 - c1)((1 - f,1 - f,1 - f) + f(1 - c2))
Which starts to make sense after a couple of minutes of reasoning and carefully following the math, giving a result that seems correct intuitively according to what we would expect the screen blend mode to do. But still I wondered: does the “official” formula do the same as mine? Or, mathematically speaking, are both expressions equivalent?
The first thing we have to do is isolating the portion of them that differ, namely:
1 - (1 - c1)((1 - f,1 - f,1 - f) + f(1 - c2))
1 - (1 - c1)(1 - c2 * f)
Now we can equal both portions and check if the equality holds. If it does, the two formulae do exactly the same. So let’s play around with the algebra:
(1 - f,1 - f,1 - f) + f(1 - c2) = 1 - c2 * f
(1 - f,1 - f,1 - f) + f - f * c2 = 1 - c2 * f
(1 - f,1 - f,1 - f) + f = 1
And finally, remembering that when talking shaders reals become a 3-vector of components “real,real,real” when working with other vectors[*]:
(1 - f,1 - f,1 - f) + f = 1
(1 - f,1 - f,1 - f) + (f,f,f) = (1,1,1)
(1,1,1) = (1,1,1)
QED
The funny thing is that I find my formula far simpler than the official one, let alone more intuitive. Does someone know why the Blender team chose their formula, or if they are even aware of this?
Have a good day!
[*] Well, not always, but they do in the cases seen in this proof.