> I know it's small enough for you to have2762907758494613432722057848250457745983.
> succeeded, but it took a MPQS implementation 51 seconds to find the
> factors 31467085354882538839727 and
Sure, MPQS gives the answer in a short time with a recent computer.
But I was just focusing on the fact that the factors of such numbers
are not obvious in general. Otherwise, it could have been used to
prove that 48^p-47^p is never prime maybe ...
Until now, the only thing one can say about them is that they are of
the form 2*k*p+1 for some integer k.