Perhaps explore plotting the Ulam spiral too? https://en.wikipedia.org/wiki/Ulam_spiral

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!?

Not exactly the same, but I made this Ulam spiral generator more than a decade ago.

https://embed.plnkr.co/mdZX6C/

It isn't just doing primes though, instead the size of the dot generated is dependent on the number of even divisors for the number at that position.

Seconding the Ulam spiral. My first thought was "why can't I see the diagonals?" because I expected it to be the Ulam spiral.

https://www.alpertron.com.ar/ULAM.HTM