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ECM-GMP query

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  • j_m_berg
    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
    Message 1 of 2 , Aug 6, 2005
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      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.
    • 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 2 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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