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Re: ECM-GMP query

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  • j_m_berg
    ... in a ... has ... will ... run ... stage-2 ... dickson ... holds ... Out of curiosity I did some minor research through trial factoring. Using F12 (12th
    Message 1 of 2 , Aug 7, 2005
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      --- In primenumbers@yahoogroups.com, "j_m_berg" <j_m_berg@y...> wrote:
      > Documentation is rather slim regarding the -power and -dickson
      > parameters. As a result, I'm attempting to determine whether these
      > parameters may be used to enhance factor discovery.
      >
      > It is implied that different power and dickson values will result
      in a
      > different set of potential factors in stage-2. Some minor testing
      has
      > proven to me that using one may give a factor, while using another
      will
      > not.
      >
      > Given the time it takes to run stage-1, would it make more sense to
      run
      > a single stage-1 (with the -save option) and then run multiple
      stage-2
      > passes (with the -resume) with different -power and -dickson values?
      >
      > If it does make sense to do this, is there certain values that make
      > more sense to try (or not try)? For example does using a large -
      dickson
      > value negate the need to use smaller -dickson values? The same
      holds
      > for the -power option.


      Out of curiosity I did some minor research through trial factoring.
      Using F12 (12th Fermat Number) and a sigma (3300588716) and B1 (2e3)
      that generated only a single factor (114689). I then used a series of
      stage-2 runs (B2=2e3-2e5) with varying -power and -dickson values
      (see table below).

      It can be seen that the results indicate that multiple stage-2 runs
      may be of-value if done with varying power/dickson values. Note that
      two different factors were found and occasional no-factors found.

      Still remaining is the question whether a sufficiently large enough
      power or dickson value would suffice as a single stage-2 pass, rather
      than multiple stage-2 passes. Notice that both dickson and power tend
      towards finding a factor (though not both factors) as their values
      increase. But since no power/dickson value produced both factors
      within the test cases, it may still be of-value to do multiple stage-
      2 passes with varying values.



      Dickson Power
      - - - - - - -
      1
      2
      3
      4 26017793
      5
      6 26017793 63766529
      7 63766529 63766529
      8 63766529
      9 63766529
      10 63766529
      11 63766529 26017793
      12 26017793 63766529
      13 63766529 63766529
      14 63766529 63766529
      15
      16 63766529 63766529
      17 63766529 63766529
      18 63766529 63766529
      19 63766529 63766529
      20 63766529 63766529
      21 63766529 63766529
      22 63766529 63766529
      23 63766529 63766529
      24 63766529 63766529
      25 63766529 63766529
      26 63766529 26017793
      27 63766529 63766529
      28 63766529 63766529
      29 63766529 63766529
      30 63766529 63766529
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