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We've mentioned Conway's Life here, just the once, and it's known that Life is Turing-complete, so structures in Life can compute things. Here's a Turing machine running on a 6502 life (needs banked RAM):


Well, Life's computers are huge, so back in the day Brian Silverman reasoned his way to Wireworld, a four-state grid universe which has 'electrons' travelling down 'wires' and which allows much more compact computers. (Mini in-browser simulator here.) And here's one such, with 64 registers and a transport-triggered architecture, which is currently programmed to compute prime numbers:


There's a link on that page to a simple C implementation of Wireworld, so I was able overnight to find a larger prime number:


More detail on how that CPU works here.