--- 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