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Re: [PrimeNumbers] Re: GFN Now Largest Known Prime?????

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  • Yves Gallot
    Proth 6.x uses the base 2 for the PRP test of GFN then all Fermat numbers were reported probable prime (and composite for N 2^4 during the verification
    Message 1 of 4 , Aug 26, 2002
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      Proth 6.x uses the base 2 for the PRP test of GFN then all Fermat numbers
      were reported probable prime (and composite for N > 2^4 during the
      verification stage).
      Because many people thought that they had discovered the new largest known
      prime by using GFN with b=2^a and N=2^(24-a), I modified this in Proth 7.x:
      if b is a power of 2, Proth uses the base 3 for the PRP test and then
      declares Fermat numbers composite during the first test.

      It was just another verification with Proth 6.x then F_24 is a base-2 PRP.

      Yves

      ----- Original Message -----
      From: "jbrennen" <jack@...>
      To: <primenumbers@yahoogroups.com>
      Sent: Monday, August 26, 2002 6:37 PM
      Subject: [PrimeNumbers] Re: GFN Now Largest Known Prime?????


      --- In primenumbers@y..., David Underbakke <david@u...> wrote:
      >
      > 9999 65536^1048576+1 5050446 g224
      >
      > Congratulations to prover g224.

      This is an obvious fake. This number is F_24 (2^2^24+1), which
      was proven composite in 1999.
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