We know that conway's game of life can support a turing machine, therefore everything that can be computed on a regular turing machine can be computed in conway's game of life. Want to know what's REALLY cool? Conway's game of life is a 2d world. [http://en.wikipedia.org/wiki/Rule_110] is a 1d world and you also can create a turing machine in it, therfore allowing you to simulate anything that we can simulate on a regular computer.
> "It works by testing whether each integer is divisible by any smaller integer, apart from itself and 1. This is similar in principle to the Sieve of Eratosthenes."
How is this anything close the the Sieve? The Sieve is forward looking eliminating number that are multiples of a found prime, forward looking and eliminating. This, from the description, is just the classic prime test of looking at all smaller numbers to find divisors.
Not only that, but it can find lowest common denominator, solve a system of linear equations, and even run the complete RSA algorithm (albeit with a pseudorandom RNG that's deterministic).
