## Goldbach Proof

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• 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
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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
Message 2 of 4 , Mar 3, 2007
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--- "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

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• ... 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
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--- 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
• ... 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
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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
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