64 Rings, and 584 Billion Years at One Move a Second
Thirty-two rings really do take 136 years at a move a second, which is what makes doubling it to 272 so tempting. The exact ratio between the two cases factors as two to the thirty-two plus one, so the guess is short by more than four billion times. The article carries the lower bound the recursion alone does not give, and the 2-adic rule for which ring moves when.