Suppose we know $2p\in(0,1)$ fraction of the bits of $PQ$ exactly where $P$ and $Q$ are primes is it possible to identify $p$ fraction of bits in each of $P,Q$ with certainty in polynomial time?

What is maximum $p\in(0,\frac12)$ such that if we know $2p\in(0,1)$ fraction of bits of $PQ$ with $P,Q$ primes it is possible to identify $p$ fraction of bits in each of $P,Q$ with certainty in polynomial time?

Suppose we know $4/5$ of the bits of $PQ$ exactly where $P$ and $Q$ are primes is it possible to identify $P,Q$ within $2/5$ of bits of $P$ and $Q$ with certainty in polynomial time?

Suppose we know $2p\in(0,1)$ fraction of the bits of $PQ$ exactly where $P$ and $Q$ are primes is it possible to identify $p$ fraction of bits in each of $P,Q$ with certainty in polynomial time?