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Re: Lucas tests with Fermat tests for free

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  • paulunderwooduk
    ... I need to amend this incarnation to 2 + 1 selfridge(s) for Grantham s RQFT as is clearly stated in C&P; The Lucas chain has to be computed first -- but
    Message 1 of 33 , May 30 12:03 AM
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      --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
      >
      >
      >
      > Paul Underwood's preprint at
      > http://www.mersenneforum.org/showpost.php?p=298027&postcount=44
      > has a rather neat observation in Section 4, which is all one
      > really needs to read to understand how Paul can do in
      > 2 selfridges what takes BPSW 1 + 2 selfridges and takes
      > Grantham 2 + 1 selfridges, using the Frobenius method of
      > Crandall and Pomerance.
      >

      I need to amend this incarnation to 2 + 1 selfridge(s) for Grantham's RQFT as is clearly stated in C&P; The Lucas chain has to be computed first -- but surely Grantham's b^((n-1)/2) can be tested first, making it 1 + 2 selfridge?

      Thanks for your comments, David. Expect a extracted paper in due course.

      My head is buried in the Lucas and Grantham's Frobenius tests sections of C&P and Jon's papers, along with your message.

      Paul
    • paulunderwooduk
      ... I compiled a better version of my code with gmp 5.0.5, on a different box running at 3.6GHz and got some better timings { 17.505s pfgw (3-prp) 1m1.986s
      Message 33 of 33 , Sep 21, 2012
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        --- In primenumbers@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:
        :
        > http://tech.groups.yahoo.com/group/primenumbers/files/Articles/

        > I ran various "minimal \lambda+2" tests on Gilbert Mozzo's 20,000 digit PRP, 5890*10^19996+2^66422-3 (x=1), using a 2.4GHz core:
        > {
        > 0m32.374s pfgw64 (3-prp)
        > 1m9.876s pfgw64 -t
        > 1m53.535s pfgw64 -tp
        > 3m0.483s pfgw64 -tc
        > 5m12.972s pfgw64 scriptify
        > 4m4.811s gmp (-O3/no pgo)
        > 4m9.148 pari-gp
        > 1m15s theoretical Woltman implementation
        > }
        >

        I compiled a better version of my code with gmp 5.0.5, on a different box running at 3.6GHz and got some better timings
        {
        17.505s pfgw (3-prp)
        1m1.986s pfgw -tp
        1m13.789s gmp (-O3/no pgo)
        }

        Paul
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