User blog comment:Edwin Shade/In The Pursuit Of Organization/@comment-1605058-20171102142430/@comment-32876686-20171102210820

You're right. Originally I had worked this out on paper, and made a mistake which led me to believe the differences of the squares of the primes eventually cycled through the values 3, 7, and 37, though that isn't so.

I am almost certain however that the diagonol of 1's in the first table never ends, but I'm willing to hear a counter-example if you have one.