Real-time generation of primes by a one-dimensional cellular automaton with 11 states

A 11-state one-dimensional cellular automaton is constructed which generates the primes in the following sense: The content of the 0-th cell at time t is equal to ‘1’ if t is a prime, and is equal to ‘0’ otherwise. The neighbourhood type of this CA is (-1, 0, 1), i.e. the most usual one. At time t = 0 only the 0-th cell is in the non-quiescent state (here ‘0’ is not the quiescent state). Further, a one-dimensional CA is constructed with the radius 12 but with two states only which also generates the primes. (At time t - 0 only the 1-st cell is in non-quiescent state.) Also a generalized Pascal triangle with 83 distinct elements is constructed which generates the odd primes in a similar sense. Hence the primes can be real-time generated also by a 83-state one-dimensional CA with the neighborhood type (-1,1).