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RE: [PrimeNumbers] MPQS again (after a few months to think about it...)

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  • Paul Leyland
    ... It s conventional to divide the quadratic residue by the large prime once relations have been combined in this manner. Divide , of course, means
    Message 1 of 3 , Aug 1 8:15 AM
      > Am I missing something here, or is my evaluation correct. If the
      > latter is true then any benefit of using PMPQS or PPMPQS is surely
      > outweighed by the fact that the eventual chance of finding a factor
      > is not 50% but maybe 12.5% or even as low as 0.78125% ?

      It's conventional to "divide" the quadratic residue by the large prime
      once relations have been combined in this manner. "Divide", of course,
      means "multiply by the multiplactive inverse". Having performed this
      operation, discard both identical copies of the large prime from the
      combined relation.

      You should find that this returns the probability back to 50%. Think
      about it!


      Paul
    • Satoshi TOMABECHI
      Your claim is that partials and partial-partials yield a little full relations. It is right in a sense. But experiments show that PMPQS or PPMPQS yield more
      Message 2 of 3 , Aug 1 8:20 PM
        Your claim is that partials and partial-partials yield
        a little full relations. It is right in a sense.
        But experiments show that PMPQS or PPMPQS yield more full relations
        than MPQS for over 70 digits.
        You have to notice that the probability yielding full relations
        >from partials is not lenear to the number of partials.
        Have you ever heard about birthday paradox?

        Satoshi Tomabechi.
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