In Blum Blum Shub, the generator is $x_{n+1}={x_n}^2 \mod M$ where $M=p \cdot q$, $p \in \mathbb P$, and $q \in \mathbb P$. Supposedly, knowing $p$ and $q$ is enough to break the system. But if I know M, I can calculate the next number in the sequence, so there is no need to know the two factors. Why isn't that sufficient?
Update: Since I wasn't think all those times I read about BBS, just ignore the part about directly calculating the next number. Instead, why would knowing the period provide an attacker with any additional information?