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

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• ... 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
"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:
with the choice of q tuned in the light of the first 3 hits.

David
• ... 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
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