So then I got the brilliant idea to not take notes, since I wasn't looking at them!
It turned out that the act of taking the notes was fixing the material in my head such that I didn't need the notes to refer back to.
all integers have a square, while not all integers are prime.
in any given span, you'll see more primes than squares, however.
more dense?
Of course the pressing question is, if this is the start field for a Conway game-of-life, do any interesting patterns evolve?
It would be fun to brute-force a few starting grid sizes and seeing how long the game continues. Games that last more than a few steps can be set aside for human evaluation.
Because if it turns out that some particular smallish grid or spiral of primes causes something interesting to happen in game-of-life, then you can imagine HN melting down!?
http://cnet.com/home/kitchen-and-household/appliance-science... verifies this.