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

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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 1 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]



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    • 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 2 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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