[Rules for the] primes cellular automaton

The rules are

{{13, 3, 13}  12, {6, _, 4}  15, {10, _, 3 | 11}  15, {13, 7, _}  8, {13, 8, 7}  13, {15, 8, _}  1, {8, _, _}  7, {15, 1, _}  2, {_, 1, _}  1, {1, _, _}  8, {2 | 4 | 5, _, _}  13, {15, 2, _}  4, {_, 4, 8}  4, {_, 4, _}  5, {_, 5, _}  3, {15, 3, _}  12, {_, x : (2 | 3 | 8), _}  x, {_, x : (11 | 12), _}  x - 1, {11, _, _}  13, {13, _, 1 | 2 | 3 | 5 | 6 | 10 | 11}  15, {13, 0, 8}  15, {14, _, 6 | 10}  15, {10, 0 | 9 | 13, 6 | 10}  15, {6, _, 6}  0, {_, _, 10}  9, {6 | 10, 15, 9}  14, {_, 6 | 10, 9 | 14 | 15} 10, {_,6|10,_} 6, {6 | 10, 15, _}  13, {13 | 14, _, 9 | 15}  14, {13 | 14, _, _}  13, {_, _, 15}  15, {_, _, 9 | 14}  9, {_, _, _}  0}

and the initial conditions consist of {10, 0, 4, 8} surrounded by 0's. The right-hand region in the pattern grows like √t. (See also page 132.)