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Comparing efficiency of factoring methods

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  • Kermit Rose
    I m wondering how my current factoring program compares to other methods used in terms of the amount of work needed to find the factors. Factored here are
    Message 1 of 2 , Aug 4, 2006
      I'm wondering how my current factoring program compares to other methods
      used

      in terms of the amount of work needed to find the factors.

      Factored here are 10^16 + 37 and 10^16+39.


      The difficulty number is the number of trial difference of squares used in
      the algorithm.

      z = 10000000000000037 x = 168040027 y = 59509631 difficulty = 1382382
      z = 10000000000000039 x = 1830629 y = 5462603291 difficulty = 655091



      Kermit < kermit@... >
    • Phil Carmody
      ... If you really wondered how it compares to other methods, why have you not compared it to other methods? Grab Miracl, and see how quickly P-1, P+1, Rho, and
      Message 2 of 2 , Aug 4, 2006
        --- Kermit Rose <kermit@...> wrote:
        > I'm wondering how my current factoring program compares to other methods
        > used in terms of the amount of work needed to find the factors.
        >
        > Factored here are 10^16 + 37 and 10^16+39.
        >
        > The difficulty number is the number of trial difference of squares used in
        > the algorithm.
        >
        > z = 10000000000000037 x = 168040027 y = 59509631 difficulty = 1382382
        > z = 10000000000000039 x = 1830629 y = 5462603291 difficulty = 655091

        If you really wondered how it compares to other methods, why have you not
        compared it to other methods?

        Grab Miracl, and see how quickly P-1, P+1, Rho, and ECM can split those
        numbers.

        168040027 will be found by P-1, and often P+1, trivially.
        59509631 will be found by P+1 trivially.
        1830629 will be found by P+1 trivially.

        Most things that P+/-1 can find trivially Rho and ECM can too.

        Phil


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