I was reading some articles about attacks on RSA system and I wonder about some generalization of the following theorem.

> 
> Theorem (Coppersmith).
> 
> 
> Let $N=pq$ be an $n$-bit RSA modulus, where
>  $p<q<2p$. Then given the $\frac{n}{4}$ least significant bits of $p$
>  (that is $\approx$ half of LSB of $p$) or the $\frac{n}{4}$ most
>  significant bits of $p$ (that is $\approx$ half of MSB of $p$), one
>  can efficiently factor $N$.
> 
> 
> 

I wonder what is going on, if we know for example $\frac{n}{8}$ MSB of $p$ **and** $\frac{n}{8}$ LSB of $p$.

Second idea, what is going on, if we know for example $\frac{n}{8}$ MSB of $p$ **and** $\frac{n}{8}$ LSB of $q$.

Is it enough for factoring $N$ in effective way? Or maybe with some other numbers instead of pair $(\frac{n}{8}, \frac{n}{8})$ (of course assuming, that both numbers are greater than $0$ and less than $\frac{n}{4}$)? Was there some research in this field?