Right, I posted some about a variation of it in this thread >>9585.
I wrote a quick function to enumerate the first row, computing the gcd with c and then a loop to iterate over multiples of c (primes from column 1). You clearly see that the factors exists in different columns of e indexes by polite numbers, but that was when I realized I had already seen this pattern in >>8973 and I was just looking at a part of that.
Once you add more factors to c the sub-factors occurs several more times, in different orders.
Another though I had about the pattern in >>8973 was that, since the squares are rotated on the diagonal maybe we can shift the e's (to straighten out the squares). Like, move the "e-line" to the diagonal. Then the squares would become straight.