## to calculate left k's

Expand Messages
• 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
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
• ... 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
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
Your message has been successfully submitted and would be delivered to recipients shortly.