Loading ...
Sorry, an error occurred while loading the content.

Goldbach Proof

Expand Messages
  • Werner D. Sand
    What do you think about the so-called proof of the Goldbach Conjecture by Jinzhu and Zaizhu Han? http://arxiv.org/ftp/math/papers/0701/0701235.pdf
    Message 1 of 4 , Mar 3, 2007
    • 0 Attachment
      What do you think about the so-called proof of the Goldbach Conjecture
      by Jinzhu and Zaizhu Han?
      http://arxiv.org/ftp/math/papers/0701/0701235.pdf
    • Phil Carmody
      ... Well, they aren t loons as they are familiar with prior work in the area; but I can t help thinking that a unary function which is defined in terms of two
      Message 2 of 4 , Mar 3, 2007
      • 0 Attachment
        --- "Werner D. Sand" <Theo.3.1415@...> wrote:
        > What do you think about the so-called proof of the Goldbach Conjecture
        > by Jinzhu and Zaizhu Han?
        > http://arxiv.org/ftp/math/papers/0701/0701235.pdf

        Well, they aren't loons as they are familiar with prior work in the area;
        but I can't help thinking that a unary function which is defined in terms of
        two unknowns is going to lead to problems:

        lambda(n) = { 0, if n==N mod p, p<=sqrt(N), (N,p)=1
        { 1, otherwise

        So, chose p such that (n,p)=1, and then set N=p^2+(n%p)
        Then p<=sqrt(N), and (N,p)=(n,p)=1

        So their lambda(n) is either trivially 0 everywhere, or misdefined.

        I am obliged now to do the following...

        When refering to papers on arXiv, please include the full arXiv reference, not
        just the URL. In the case of the above, it's
        <<<
        math.GM/0701235 :
        Title: A Proof of Goldbach Conjecture
        Authors: Jinzhu Han, Zaizhu Han
        >>>

        Which tells us that it's in the 'maths' section, and in particular is in the
        'Garbage Machine', which is presumably what 'GM' stands for.

        TYVM, HTH, HAND,
        Phil

        () ASCII ribbon campaign () Hopeless ribbon campaign
        /\ against HTML mail /\ against gratuitous bloodshed

        [stolen with permission from Daniel B. Cristofani]



        ____________________________________________________________________________________
        TV dinner still cooling?
        Check out "Tonight's Picks" on Yahoo! TV.
        http://tv.yahoo.com/
      • Mike Oakes
        ... Conjecture ... [I typed a reply on the website about 2 hours ago but must have hit the wrong key as it seems to have disappeared into the ether without
        Message 3 of 4 , Mar 3, 2007
        • 0 Attachment
          --- In primenumbers@yahoogroups.com, "Werner D. Sand"
          <Theo.3.1415@...> wrote:
          >
          > What do you think about the so-called proof of the Goldbach
          Conjecture
          > by Jinzhu and Zaizhu Han?
          > http://arxiv.org/ftp/math/papers/0701/0701235.pdf
          >

          [I typed a reply on the website about 2 hours ago but must have hit
          the wrong key as it seems to have disappeared into the ether without
          trace.
          Apolgies if it also turns up some time.] I wrote something like this:

          Their whole claim to a proof rests on the statement made after their
          eqn. (1.6):
          if pi(N,lambda) > 0 (for all N), then GC is true.

          I think this is claimed implication is false.

          Take a particular example: N = 10.

          Then their definition of lambda(n), eqn. (1.1), says that
          lambda(n) = 0 if n = 1 mod 3, else 1.

          By (1.3),
          pi(N,lambda) = sum_{p <= N} lambda(p)
          = lambda(3) + lambda(5) + lambda(7)
          = 1 + 1 + 0.

          This is indeed > 0 but so what?
          That's NOT the same as the fact that there are primes p1 and p2 < 10
          such that
          p1 + p2 = 10.

          So, proving that pi(N,lamda) > 0 for all (sufficiently large) N,
          which they MAY have done (giving the benefit of the doubt to their
          rather difficult proof steps), is NOT equivalent to proving Goldbach.

          Moreover, GC is for /all/ N, not just for large N, and since their
          proof steps only apply for large N they fall down on that score, at
          the very least.

          -Mike Oakes
        • Jens Kruse Andersen
          ... After briefly looking at later parts, I guess misdefined. When defining lambda(n), they probably assume N is an already given constant (the number they
          Message 4 of 4 , Mar 3, 2007
          • 0 Attachment
            Phil Carmody wrote:
            > --- "Werner D. Sand" <Theo.3.1415@...> wrote:
            > > What do you think about the so-called proof of the Goldbach
            > > Conjecture by Jinzhu and Zaizhu Han?
            > > http://arxiv.org/ftp/math/papers/0701/0701235.pdf
            >
            > Well, they aren't loons as they are familiar with prior work in
            > the area; but I can't help thinking that a unary function which
            > is defined in terms of two unknowns is going to lead to problems:
            >
            > lambda(n) = { 0, if n==N mod p, p<=sqrt(N), (N,p)=1
            > { 1, otherwise
            >
            > So, chose p such that (n,p)=1, and then set N=p^2+(n%p)
            > Then p<=sqrt(N), and (N,p)=(n,p)=1
            >
            > So their lambda(n) is either trivially 0 everywhere, or misdefined.

            After briefly looking at later parts, I guess misdefined.
            When defining lambda(n), they probably assume N is an already given
            constant (the number they want to write as sum of two primes), while
            p can be any prime.
            Under this assumption, if n < N and lambda(n) = 1, then N-n is prime.
            I will not review the paper.

            --
            Jens Kruse Andersen
          Your message has been successfully submitted and would be delivered to recipients shortly.