Let it be $p, q \in \mathbb{P}$ with $p,q \in [2^{b-1}, 2^b]$ for some $b \in \mathbb{N}$ and $p \cdot q = n \in \mathbb{N}$. What would be the distance between $p$ and $q$ (as a function of b) so that the factorization of $n$ is hardest or be considered difficult?
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