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RE: [PrimeNumbers] ECM, sigma of 5

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  • Torbjörn Alm
    The sigma values 0,1,5 are not allowed for the calculation of a proper starting value of the elliptic curve. See Prime Numbers (C&P) , page 305, Theorem 7.4.3.
    Message 1 of 2 , Sep 20, 2004
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      The sigma values 0,1,5 are not allowed for the calculation of a
      proper starting value of the elliptic curve.
      See Prime Numbers (C&P) , page 305, Theorem 7.4.3.

      Torbjörn Alm

      > -----Original Message-----
      > From: Jay Berg [mailto:jberg@...]
      > Sent: den 20 september 2004 19:14
      > To: primenumbers@yahoogroups.com
      > Subject: [PrimeNumbers] ECM, sigma of 5
      >
      >
      >
      > There's no way I'll ever figure this out - given my limited amount of
      > math. But maybe someone else can figure it and decide whether it's of
      > any interest.
      >
      > I was poking at Fermat Numbers using ECM-GMP (latest version) and
      > noticed something that struck me as odd. It appears that if a sigma
      > of 5 is used on any Fermat Number, ECM-GMP always "finds" a factor
      > equal to the input N value.
      >
      > It's obviously something to do with the implementation of ECM, but
      > I've no idea why this is so consistant nor why it should happen. I've
      > tried sigma values 2-32000 and 5 is the only sigma value that results
      > in N being "found".
      >
      >
      >
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