Encountering this by chance is exceedingly unlikely of course, if p and q are randomly generated. In probability terms it amounts to the first half of p (or q) all being zero (apart from a leading 1) so roughly 2^(-n/4) where n is the bit size of n. So for RSA 2048 the probability of this happening is on the order of 2^-512, or in base-10 terms 0.0000000...0000001, with roughly 150 zeros before the one!
if N=p*q and p-q < sqrt(p) then its easy to factor