What I said back near the start is this is about working backwards.
One of the approaches out of the solutions to P=NP is the quasi-faith approach. Bear with me.
Let's ASSUME (or have Faith) for now, that the solution to the integer factorisation is O(log q) where q is the length of the binary representation of c in bits. And log q is the natural log of q.
The first step (as ALL steps) will grow in size as the length of c increaases, as will ALL the steps.
HOWEVER, the step (and ALL steps) cannot grow in size (of computation) greater than O(log q). That's how Big Oh works.
So, EVERY step in the solution MUST obey this rule.
In other words, every step must be as hard or simpler than find the root of a large number.
The FIRST step is we admit we are powerless over c as it is, and as it stands our life becomes unmanageable in finding a and b from c as it stands. Solution, we find the root of c and the remainder and then the difference between the sum of twice the root and one (giving us f).
The second STEP is finding the family that c belongs to. This must not be harder than finding the root of c. This is the step you are stuck on.
Look at the density of entries for n under columns 59 and 61 (where e = 59 and/or 61). Prime pairs are often around HIGHLY divisible numbers. But also look further out from the central prime (for pairs, not always perfect pairs). These are families. These grow like fractals along the positive number line in the grid.
As the size of c grows, these families grow close to the natural log of the increase. These families grow and exist in a fractal pattern. You can see it in some of the images of the grid as bitmaps.