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25383RE: Yet another factoring puzzle

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  • j_chrtn
    Sep 18, 2013
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      --- In primenumbers@yahoogroups.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
      >> 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 ?


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