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First known prime factor of Fermat number F14

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  • alpertron
    Tapio Rajula posted a few days ago in http://www.mersenneforum.org/showthread.php?t=13051 (Mersenne
    Message 1 of 4 , Feb 11, 2010
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      Tapio Rajula posted a few days ago in
      http://www.mersenneforum.org/showthread.php?t=13051
      <http://www.mersenneforum.org/showthread.php?t=13051> (Mersenne forum)
      that he found a prime factor of F14:
      116928085873074369829035993834596371340386703423373313

      Best regards,

      Dario Alpern



      [Non-text portions of this message have been removed]
    • Chris Caldwell
      To add some context: F_14 = 2^(2^14)+1 was shown to be composite in 1963 by John Selfridge and Alexander Hurwitz. It took two-score and seven years to
      Message 2 of 4 , Feb 11, 2010
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        To add some context: F_14 = 2^(2^14)+1 was shown to be composite in
        1963 by John Selfridge and Alexander Hurwitz. It took two-score and
        seven years to actually find a factor. (This factor by Rajala and
        Woltman is the first known factor; and the cofactor is composite.)

        F_12 is the smallest Fermat with an incomplete factorization and F_20 is
        the smallest with no known factor.

        Happy factoring!


        -----Original Message-----
        From: primenumbers@yahoogroups.com [mailto:primenumbers@yahoogroups.com]
        On Behalf Of alpertron
        Sent: Thursday, February 11, 2010 11:50 AM
        To: primenumbers@yahoogroups.com
        Subject: [PrimeNumbers] First known prime factor of Fermat number F14


        Tapio Rajula posted a few days ago in
        http://www.mersenneforum.org/showthread.php?t=13051
        <http://www.mersenneforum.org/showthread.php?t=13051> (Mersenne forum)
        that he found a prime factor of F14:
        116928085873074369829035993834596371340386703423373313

        Best regards,

        Dario Alpern



        [Non-text portions of this message have been removed]



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      • Pavlos S
        Indeed, this is a remarkable discovery!Congratulations for the finding. ... From: Chris Caldwell Subject: RE: [PrimeNumbers] First known
        Message 3 of 4 , Feb 11, 2010
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          Indeed, this is a remarkable discovery!Congratulations for the finding.

          --- On Thu, 2/11/10, Chris Caldwell <caldwell@...> wrote:

          From: Chris Caldwell <caldwell@...>
          Subject: RE: [PrimeNumbers] First known prime factor of Fermat number F14
          To: primenumbers@yahoogroups.com
          Date: Thursday, February 11, 2010, 8:43 PM
















           









          To add some context: F_14 = 2^(2^14)+1 was shown to be composite in

          1963 by John Selfridge and Alexander Hurwitz. It took two-score and

          seven years to actually find a factor. (This factor by Rajala and

          Woltman is the first known factor; and the cofactor is composite.)



          F_12 is the smallest Fermat with an incomplete factorization and F_20 is

          the smallest with no known factor.



          Happy factoring!



          -----Original Message-----

          From: primenumbers@ yahoogroups. com [mailto:primenumbers@ yahoogroups. com]

          On Behalf Of alpertron

          Sent: Thursday, February 11, 2010 11:50 AM

          To: primenumbers@ yahoogroups. com

          Subject: [PrimeNumbers] First known prime factor of Fermat number F14



          Tapio Rajula posted a few days ago in

          http://www.mersenne forum.org/ showthread. php?t=13051

          <http://www.mersenne forum.org/ showthread. php?t=13051> (Mersenne forum)

          that he found a prime factor of F14:

          1169280858730743698 2903599383459637 1340386703423373 313



          Best regards,



          Dario Alpern



          [Non-text portions of this message have been removed]



          ------------ --------- --------- ------



          Unsubscribe by an email to: primenumbers- unsubscribe@ yahoogroups. com

          The Prime Pages : http://www.primepag es.org/



          Yahoo! Groups Links






























          [Non-text portions of this message have been removed]
        • djbroadhurst
          ... Thanks, Dario, for communicating Tapio Rajala s grand discovery. I remark that http://www.prothsearch.net/fermat.html is still consistent with the (to me,
          Message 4 of 4 , Feb 12, 2010
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            --- In primenumbers@yahoogroups.com,
            "alpertron" <alpertron@...> wrote:

            > a prime factor of F14:
            > 116928085873074369829035993834596371340386703423373313

            Thanks, Dario, for communicating Tapio Rajala's grand discovery.

            I remark that http://www.prothsearch.net/fermat.html
            is still consistent with the (to me, quite bizarre)
            conjecture that omega(2^(2^n)+1) is a non-decreasing
            function of n.

            Can anyone please tell me who dreamed up that still
            unfalsified conjecture? More importantly, was there ever the
            remotest hint of an heuristic argument? Or was this merely
            blatant exploitation of the law of small numbers?

            Best regards

            David Broadhurst
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