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Topic: Goldbach Conjecture and Schnirelmann's "300,000 primes"
Replies: 11   Last Post: Mar 1, 2010 6:00 PM

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drobotv@gmail.com

Posts: 14
Registered: 5/21/07
Re: Goldbach Conjecture and Schnirelmann's "300,000 primes"
Posted: Jan 19, 2010 9:30 AM
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On Jan 17, 6:00 pm, "mwatk...@maths.ex.ac.uk"
<mwatk...@maths.ex.ac.uk> wrote:
> > The earlier bound (for the full S'nirel'man constant) I know
> > is 2.10^{10} by  Êeptickaja in 1963

>
> Thanks for the clarification!
>
> Incidentally, the Schnirelmann paper which I mentioned as the source
> for the "300000" claim
> [Uspekhi Math. Nauk 6, 3-8, 1939]
> turns out to be his obituary.
>
> I found a PDF of the Russian original here:http://tinyurl.com/yzzk9ln
>
> If someone who can read Russian can be bothered, I'd be interested to
> know if it does actually make this claim.  I'm interested in this more
> from an historical, rather than a number theoretical, perspective.
>
> Thanks,
> MW


I don't think the obituary makes the claim about 300,000. i.e., the
claim that every even number can be
represented as a sum of at most 300,000 primes. In a couple of days
I'll make the translation of the obituary available
on line, (it is 6 pages long), but as far as I can tell there is no
mention about the number 300,000 there. What it says about the
Goldbach conjecture is that there a fixed number X, such that every
sufficiently large integer (even or odd)
can be expressed as a sum of at most X primes, but there is no mention
of the value of X. The way Schnirelmann
shows that is to prove that the set {p+q | p, q primes} has a positive
density.

As ever,


Vlad


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