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Re: Naive question on 2^1896-1

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  • elevensmooth
    ... Do you just want the factors, or do you want to learn how to find the factors? If you just want the factors, you can use Alpertron at
    Message 1 of 6 , Jun 12, 2007
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      --- In primenumbers@yahoogroups.com, "Kevin" <research@...> wrote:
      >
      > I'm trying to factor the last part of 2^1896-1 or:
      >
      > 72009645598802661741572237135153453757864421072572019369424603012486080
      > 97428061518078682794754267412326389601722982929011560986986540564455161
      > 820809601187482593072913719887735073


      Do you just want the factors, or do you want to learn how to find the
      factors?

      If you just want the factors, you can use Alpertron at

      http://www.alpertron.com.ar/ECM.HTM

      which knows about algebraic factors and knows about the tables of
      known factors for numbers of this form. If you want to know how to
      find the factors, you need to learn about algebraic factors and the
      various factor lists. There is a discussion of Algebraic Factors in
      the Cunningham Book, available online, and in the ElevenSmooth FAQ.
      The needed factors are in Will Edgington's Mersenne factors lists
      (2^n-1) and also Richard Brent's factor lists (a^n +/- 1 for a<10000
      n<10000).
    • Kevin Acres
      ... From: elevensmooth [mailto:elevensmooth@yahoo.com] Sent: 12 June 2007 22:57 To: primenumbers@yahoogroups.com Subject: [PrimeNumbers] Re: Naive question on
      Message 2 of 6 , Jun 12, 2007
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        -----Original Message-----
        From: elevensmooth [mailto:elevensmooth@...]
        Sent: 12 June 2007 22:57
        To: primenumbers@yahoogroups.com
        Subject: [PrimeNumbers] Re: Naive question on 2^1896-1

        --- In primenumbers@yahoogroups.com, "Kevin" <research@...> wrote:
        >
        > I'm trying to factor the last part of 2^1896-1 or:
        >
        > 72009645598802661741572237135153453757864421072572019369424603012486080
        > 97428061518078682794754267412326389601722982929011560986986540564455161
        > 820809601187482593072913719887735073


        > Do you just want the factors, or do you want to learn how to find the
        > factors?

        Hi,

        The question arises from the results of a program I have that diverged from
        the Wieferich search.

        Basically it finds composite Mersenne numbers and a large composite or prime
        (if you're lucky) that divides it.

        A better example than the previous one is where the program output shows:

        2869070461631637574244868351418889546260799144254581951743734382009219393441
        76261145611475682317574468979232833614978133229351

        divides 2^19071324012257094604424955-1

        Which isn't much of a find since the above number actually divides 2^795-1.

        So basically an hours running throws up a lot of large primes, it's just
        unfortunate that nearly all already exist in lowM.txt or are trivially found
        on Alpertron.

        The premise is that it's very easy to produce thousands of large primes or
        composites that divide a range of Mersenne numbers. What isn't easy is to
        find a prime that isn't already known. Rather than attempt to factor a
        specific number it produces a number that it knows will factor some Mersenne
        number.

        Still, I'll spend a while tuning the program and see if anything new pops
        up.

        Kevin.
      • N.L.
        Hello, I have found in few seconds with my program: 2^1896 have prime factor 201487636602438195784363 I don t know, this factor are known ? regards
        Message 3 of 6 , Jun 13, 2007
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          Hello,
          I have found in few seconds with my program:

          2^1896 have prime factor 201487636602438195784363

          I don't know, this factor are known ?

          regards

          __________________________________________________
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        • elevensmooth
          ... All factors of 2^1896-1 are known. The simplest way to check that is to use the Alpertron Java factoring applet at http://www.alpertron.com.ar/ECM.HTM
          Message 4 of 6 , Jun 13, 2007
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            --- In primenumbers@yahoogroups.com, "N.L." <nluhn@...> wrote:

            > 2^1896 have prime factor 201487636602438195784363
            >
            > I don't know, this factor are known ?

            All factors of 2^1896-1 are known. The simplest way to check that is
            to use the Alpertron Java factoring applet at
            http://www.alpertron.com.ar/ECM.HTM

            William
            Poohbah of OddPerfect.org
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