Two days. Two days I'm working to find a bloody number. First I tried with brute force searching. But because that appeared not very feasible, I had to think of a more clever way to find it. Which I did. No brute force exhaustive search, just some matrix multiplication stuff.

And the number is 4212320.


By the way: it's the number of unique binary patterns of 5 by 5 pixels, ignoring all copies due to rotations and reflections. Seems a very simple problem, but it was a very tough nut to crack.