Re: [PrimeNumbers] Re: number of selfridges?
- --- On Fri, 1/27/12, WarrenS <warren.wds@...> wrote:
> > Mod(Mod(1,n)*(l+2),l^2-x*l+1)^(n+1)==2*x+5Apparenty you are not familiar with one of the linguae francae
> --what is Mod(1,n)?
on this list, namely that of Pari/GP. As Pari/GP is portable,
trivially available, and free, it stands out as one of the most
popular languages we use. It's perfect for prototyping.
The above is the notation it uses to represent elements of a ring
defined by modular reduction.
> (And by the way, do you mind not being a total jerk by using theYou might consider simply using a font that makes different characters
> letter l which is visually almost the same as the number 1?
look, erm, different.
You might also consider moderating your tone. I know from your private
e-mails that you find that hard, but can you please try harder on-list?
You clearly have many intersting mathematical ideas to share, they're
best not clouded by such noise.
- --- In email@example.com, "paulunderwooduk" <paulunderwood@...> wrote:
>Combining fails with the composite counterexample n=256999 and x=32768, However, I have tested the 1+1+1+2 conjecture up to n<10^7,
> --- In firstname.lastname@example.org, "paulunderwooduk" <paulunderwood@> wrote:
> > Hi,
> > I have added a Fermat test to make a 1+1+1+2 selfridge test:
> > For N>5, with gcd(6,N)==1, find an integer x:
> > gcd(x^3-x,N)==1
> > kronecker(x^2-4,N)==-1
> > and check:
> > (x+2)^((N-1)/2)==kronecker(x+2,N) (mod N) (Euler)
> > (x-2)^((N-1)/2)==kronecker(x-2,N) (mod N) (Euler)
> > x^(N-1)==1 (mod N) (Fermat)
> > L^(N+1) == 1 (mod N, L^2-x*L+1) (Lucas)
> Note: I should say gcd(30,N)==1 because gcd(x^3-x,N)==1 and kronecker(x^2-4,n)==-1.
> Re: http://tech.groups.yahoo.com/group/primenumbers/message/24090?l=1
> Now consider combining the 2 Euler tests with the Lucas test:
> (L*D)^((n+1)/2)==D (mod N, L^2-x*L+1) (D=x^2-4.)
> with the restriction kronecker(x+2,N)==-1.
> These together with the Fermat test makes for a 1+2-selfridge test.
> Can you find a counterexample?
> So far the near-refutation from Pinch's carmichael list is:
> 1909001 884658 1909001
Paul -- restoring symmetry