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Re: Goldbach Conjecture and Schnirelmann's "300,000 primes"
Posted:
Jan 19, 2010 9:30 AM


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, 38, 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
=================== * Vladimir Drobot * Retired and gainfully unemployed * http://www.vdrobot.com * mailto:drobot@pacbell.net ==================



