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puzzle for a counterexample

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  • bhelmes_1
    A beautifull day, i am looking for a counterexample concerning the following prime test: 1. Let jacobi (a, p) = -1 and a^[(p-1)/2]=-1 mod p 2 if (a+sqrt
    Message 1 of 66 , Oct 8, 2012
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      A beautifull day,

      i am looking for a counterexample concerning the following prime test:

      1. Let jacobi (a, p) = -1 and a^[(p-1)/2]=-1 mod p
      2 if (a+sqrt (a))^p = a-sqrt(a) mod p then p is prime

      This is a combined p-1 and p+1 test with 1+3 selfridges.

      Nice Greetings from the Primes
      Bernhard
    • 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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