I haven't understood why the last proposition holds. Why isn't it possible to make $\Omega(p_0)$ repetitions, given that the size of $p_0$ is smaller than this of n ? @SEJPM
And we say that it is hard when $p_0$ has more than 20 decimal digits, because it is difficult to find a non-trivial factor of n, when its smallest divisor has more than 20 digits? @SEJPM