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Notable factorizations

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  • d.broadhurst@open.ac.uk
    A Konyagin-Pomerance proof of (1721^2161-1)/1720 6990 x32 01 Generalized repunit by Broadhurst, de Water and Leyland, is detailed in
    Message 1 of 1 , Nov 1, 2001
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      A Konyagin-Pomerance proof of

      (1721^2161-1)/1720 6990 x32 01 Generalized repunit

      by Broadhurst, de Water and Leyland, is detailed in

      http://groups.yahoo.com/group/primenumbers/files/Factors/dls1721c.txt

      It entailed two notable factorizations:

      Phi(108,1721) = 757 * 2377 * 67641587029 *
      70633277924977308401493092426879984788577991577 *
      p53

      Phi(180,1721) = 12601 * 10968736861 *
      133421611918311060830710245059272984140145279181721541 *
      p89

      The first was achieved by Tomabechi SNFS, which took
      4 CPU days on a 1GHz Athlon, with zero hand-holding.
      Thanks Satoshi!

      Paul Leyland repeated the feat in less than 1 CPU day,
      using Peter Montgomery's code, for which the
      hand-holding cost is understandably greater.

      The second factorization took about 1 CPU month,
      spread over a variety of Paul's machines.

      David Broadhurst
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