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

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  • paulunderwooduk
    ... My UTM bio page has been updated, now linking these counterexamples too. I have been trying to get big GCD plus CRT working in GP. I am wondering if my
    Message 1 of 66 , Oct 21, 2012
      --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
      >
      >
      >
      > --- In primenumbers@yahoogroups.com,
      > "paulunderwooduk" <paulunderwood@> wrote:
      >
      > > I have linked your counterexamples to my only remaining
      > > single-Lucas test on my UTM bio page:
      > > http://primes.utm.edu/bios/page.php?id=181
      > > This test also appears in my paper.
      >
      > I tuned the code to find 8 counterexamples in 15 minutes:
      >
      > [226437979, 4683227]
      > [342055369, 50400111]
      > [1894955311, 169658692]
      > [1920594079, 307611949]
      > [3894053311, 1591613985]
      > [9347580631, 1197787149]
      > [10194250691, 1999795690]
      > [18885022511, 3905986652]
      >
      > I did not use any tables, but if you care to google
      > 226437979 pseudoprime
      > .... down to ....
      > 18885022511 pseudoprime
      > you may find all 8 documented, in one capacity or another.
      >

      My UTM bio page has been updated, now linking these counterexamples too.

      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,

      Paul
    • 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
        --- 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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