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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'.

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Is there one that generates all primes? That would seem to be a less specialized place to start. – mjqxxxx Oct 2 '12 at 21:09
@mjqxxxx : Well there are such because of the universality of cell auto. But if there exist such simple ones is another matter. I believe the answer to that is also yes. I believe I have seen such but Im not sure. Was there an example of that in NKS ? Maybe I saw it there. – mick Oct 2 '12 at 21:16
Right, I meant a simple, potentially non-universal one, like you're asking about here. – mjqxxxx Oct 2 '12 at 21:37

Sure, there is one for prime numbers in wolfram's site:

Source Code is also available on the right side of the page.

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Thanks , but I have no permission to the source code. Could you give it here ? Also Im not so good with code, maybe you can explain the rule ? Like in rule 30 or such. – mick Oct 3 '12 at 12:30
@mick You can go here for the sourcecode. – Sniper Clown Oct 10 '12 at 2:12
Thanks Mahmud +1 But I do not understand the math behind it. ( Im not so good with code either ) – mick Oct 11 '12 at 11:57
I think that this is the author: you might want to contact him, perhaps he could father explain the logic. – Sonia Oct 14 '12 at 9:19
It seems this is the classical construction by P. C. Fischer : P.C. Fisher "Generation on primes by one dimentional real time iterative array" J. ACM, 12 (1965), pp. 388–394 – user148606 May 8 '14 at 16:13

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