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to calculate left k's

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  • Norman Luhn
    Hello members, is it known ? I have found a formula to calculate left k s with n conditions. It is interest for finding the optimum of sieving. Example: We
    Message 1 of 66 , Oct 18, 2012
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      Hello members,

      is it known ? I have found a formula to calculate left k's with n
      conditions. It is interest for finding the optimum of sieving.

      Example:
      We have 2000000 k's left and it was sieving primes until p=10^9.
      Conditions are n=8. How many k's are left up to p=2*10^12 ?

      Calculate now : ( ln((10^9)^2 ) / ln((2*10^12)^2 ) ) ^8 * 2000000 =
      164200 k's left.

      You can test it with NewPgen. ( CC , 4 tuplets , etc )

      regards

      Norman
    • 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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