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## puzzle for a counterexample

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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
Message 1 of 66 , Oct 8, 2012
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
• ... 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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