>But now, J-L, are you able to explain my comment:

>

>> What is remarkable about this exercise is that it can be

>> solved so quickly. Heuristically, that was not to be expected.

>

>Can you quantify my suprise?

>

Well, I would say that for n >= 600, both algebraic factors are more than 415 digits and trial factoring them with pfgw up to 20000000 with -d option you may remove a 20000000-smooth composite factor of say 10 or 15 digits. This leave 2 factors of more than 400 digits. The "probability" for one such factor to be prime is roughly 1/l(10^400), that is about 0.001. So for both factors to be prime the probability is about 0.000001.

Am I right ?

Amicalement,

J-L