Is there a 'simple' 2 dimensional cellular automaton to generate all prime twins ?
With 'simple' I mean not too many states per cell and not so many rules. Thus a universal turing machine equivalent cellular automaton is not 'simple'.
Sure, there is one for prime numbers in wolfram's site: http://demonstrations.wolfram.com/PrimeGeneratingCellularAutomaton/
Source Code is also available on the right side of the page.