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Re: puzzle for a counterexample

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  • djbroadhurst
    ... Then they found a speed-up by a factor of 7. It now takes 2.0 milliseconds, on average, to generate a counterexample with about 20 decimal digits, running
    Message 1 of 66 , Nov 5, 2012
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      --- In primenumbers@yahoogroups.com,
      "djbroadhurst" <d.broadhurst@...> wrote:

      > In 3.5 GHz-hours, the gremlins found 33,445 counterexamples.

      Then they found a speed-up by a factor of 7. It now takes
      2.0 milliseconds, on average, to generate a counterexample
      with about 20 decimal digits, running at 3 GHz. The 6 MB file
      http://physics.open.ac.uk/~dbroadhu/cert/underbh6.txt.gz gives
      308619 counterexamples in underbh6.txt : 46% with n = 1 mod 4

      David
    • djbroadhurst
      ... Here are some scores out of 5: {A(k,x)=sum(j=0,k/2,(-1)^j*binomial(k-j,j)*x^(k-2*j));} {B(k,x)=sum(j=0,(k-1)/2,(-1)^j*binomial(k-j-1,j)*x^(k-2*j-1));}
      Message 66 of 66 , Nov 22, 2012
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        --- In primenumbers@yahoogroups.com,
        paulunderwooduk" <paulunderwood@...> wrote:

        > At least one of the evaluations of x at -1,1,0,-2 or 2
        > should be -1,1,0,-2, or 2

        Here are some scores out of 5:

        {A(k,x)=sum(j=0,k/2,(-1)^j*binomial(k-j,j)*x^(k-2*j));}
        {B(k,x)=sum(j=0,(k-1)/2,(-1)^j*binomial(k-j-1,j)*x^(k-2*j-1));}
        {L=[-1,1,0,-2,2];S=Set(L);for(k=2,40,f=factor(A(k,x)-B(k,x))[,1];
        g=f[#f];c=0;for(j=1,#L,if(setsearch(S,subst(g,x,L[j])),c++));
        print1(c","));}

        4,4,3,4,4,4,4,4,4,4,4,3,4,4,4,5,4,4,4,4,5,4,4,4,4,5,4,4,4,5,5,4,4,4,4,4,5,4,3,

        David
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