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Re: Lucas super-pseudoprimes for Q <> 1

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  • djbroadhurst
    ... It can be done a shade faster than that: {ncarm(n)=local(F=factor(n),f=F[,1],m=#f,p,t,d);if(m 3&& sum(j=1,m,F[j,2])==m,t=1;for(j=1,m,p=f[j];if((n-1)%(p-1),
    Message 1 of 46 , Nov 6, 2010
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      --- In primenumbers@yahoogroups.com,
      "mikeoakes2" <mikeoakes2@...> wrote:

      > I have a cunning script which found these first
      > 7 non-Carmichaels in 9313 msecs.

      It can be done a shade faster than that:

      {ncarm(n)=local(F=factor(n),f=F[,1],m=#f,p,t,d);if(m>3&&
      sum(j=1,m,F[j,2])==m,t=1;for(j=1,m,p=f[j];if((n-1)%(p-1),
      if((n-1)%(p+1)==0&&(n+1)%(p-1)==0,d++,t=0;break()))));t&&d;}

      {forstep(n=1,4638985,2,if(n%3&&ncarm(n),print1(n",")));
      print("took "gettime" ms");}

      507529,1080905,1739089,1992641,2110159,4013569,4638985,took 7187 ms

      Is the above, in essence, your conjectural method?

      David
    • djbroadhurst
      ... http://physics.open.ac.uk/~dbroadhu/cert/dbmo116.out gives my 116, in the format [n, factors, number of solutions] With n
      Message 46 of 46 , Nov 9, 2010
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        --- In primenumbers@yahoogroups.com,
        "mikeoakes2" <mikeoakes2@...> wrote:

        > > My revised count up to 2*10^10 is 116.
        > My (original) count up to 2*10^10 was 105.
        > So it must have missed 11, i.e. a bigger proportion.

        http://physics.open.ac.uk/~dbroadhu/cert/dbmo116.out
        gives my 116, in the format [n, factors, number of solutions]

        With n < 2*10^10, the record-holder for the number of solutions is
        [2214495361, [13, 17, 23, 29, 83, 181], 147407]
        which googles quite nicely, linking to
        http://www.cs.rit.edu/usr/local/pub/pga/fibonacci_pp

        David
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