25383RE: Yet another factoring puzzle
- Sep 18, 2013--- In email@example.com, <david.broadhurst@...> wrote:>But now, J-L, are you able to explain my comment:
>> What is remarkable about this exercise is that it can be>Can you quantify my suprise?
>> solved so quickly. Heuristically, that was not to be expected.
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 ?
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