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Re: [PrimeNumbers] Re: number of selfridges?

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  • Phil Carmody
    ... Apparenty you are not familiar with one of the linguae francae on this list, namely that of Pari/GP. As Pari/GP is portable, trivially available, and free,
    Message 1 of 46 , Jan 28, 2012
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      --- On Fri, 1/27/12, WarrenS <warren.wds@...> wrote:
      > > Mod(Mod(1,n)*(l+2),l^2-x*l+1)^(n+1)==2*x+5
      >
      > --what is Mod(1,n)?   

      Apparenty you are not familiar with one of the linguae francae
      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.

      Packages/source: http://pari.math.u-bordeaux.fr/download.html
      Docs: http://pari.math.u-bordeaux.fr/doc.html

      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 the
      > letter l which is visually almost the same as the number 1?

      You might consider simply using a font that makes different characters
      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.

      Phil
    • paulunderwooduk
      ... Combining fails with the composite counterexample n=256999 and x=32768, However, I have tested the 1+1+1+2 conjecture up to n
      Message 46 of 46 , Apr 14 10:19 AM
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        --- In primenumbers@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:
        >
        >
        >
        > --- In primenumbers@yahoogroups.com, "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:
        > N,x,gcd(x^2-1)
        > ------------------
        > 1909001 884658 1909001
        >
        > Paul
        >

        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,

        Paul -- restoring symmetry
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