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Re: many 1+1+1+2 selfridge tests

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  • djbroadhurst
    ... The gcd of p-1 and q-1 was chosen for help with the 3 Fermat tests in your 1+1+1+2 method. Then one has to keep slogging to be lucky enough to satisy one
    Message 1 of 66 , Oct 21, 2012
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      --- In primenumbers@yahoogroups.com,
      "paulunderwooduk" <paulunderwood@...> wrote:

      > I have been trying to get big GCD plus CRT working in GP.
      > I am wondering if my double-Lucas tests can be attacked with
      > such methods

      The gcd of p-1 and q-1 was chosen for help with
      the 3 Fermat tests in your 1+1+1+2 method. Then one
      has to keep slogging to be lucky enough to satisy
      one strong Lucas test. Two strong Lucas tests seemed
      too tough for my gremlins: hence their industrial action.

      The 5-selfridge craking code is here:
      http://physics.open.ac.uk/~dbroadhu/cert/underw5x.gp
      with the choice of q tuned in the light of the first 3 hits.

      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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