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Prime Fib/Luc

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  • Shane
    As a follow up, I noticed that potential factors of F(p)and L(p). Factors of F(p), must be 1,or 5 mod 8. Factors of L(p), must be 1,or 4 mod 5. Mersenne
    Message 1 of 2 , Nov 2, 2001
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      As a follow up, I noticed that potential factors of F(p)and L(p).

      Factors of F(p), must be 1,or 5 mod 8.
      Factors of L(p), must be 1,or 4 mod 5.

      Mersenne factors must be 1,or 7 mod 8.
      Along with other similar properties, this allows GIMPS to eliminate
      95% of potential factors.

      Then they use a binary algorithm, to test the rest....
      Hmmmm... can we find and algorithm ?
    • d.broadhurst@open.ac.uk
      Shane Findley wrote ... I fear you may be whistling in the wind if you hope that the likes of Lucas, Carmichael, Lehmer, Brillhart, Montgomery and Silverman
      Message 2 of 2 , Nov 2, 2001
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        Shane Findley wrote

        > Hmmmm... can we find and algorithm ?

        I fear you may be whistling in the wind
        if you hope that the likes of Lucas, Carmichael,
        Lehmer, Brillhart, Montgomery and Silverman
        missed a proof method in the Fib/Luc sector
        comparable to that which exists in the Mersenne sector.

        I'll happily bet one of Hans's mythical Groschen
        (a.k.a. dimes) that Bouk's 21925-digit PrP F(104911)
        has no proof remotely as simple as that for
        the comparably sized 2^86243-1.

        Please bear in mind that Pfgw disposes of the latter
        very quickly, merely by using the triviality of N+1,
        without invoking the more efficient Lucas-Lehmer proof
        of GIMPS.

        David
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