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Re: Schnirelmann (Was Re: Goldbach Conjecture and Schnirelmann's "300,000 primes")
Posted:
Mar 1, 2010 6:00 PM


As promised, I offer here a translation of an article about L. G. Schnirel'mann, written by V. Tikhomirov and V. Uspenskii. It appeared in the Russian magazine Kvant in 1996, No 2. pp. 26. The translation took longer than I expected, (for various reasons, mainly laziness), but here it is. The article is ostensibly written for high school students, and in a good year there maybe 5 such students on the planet who would understand and follow most of it. But, it can be read with interested and profit by a typical Ph. D. and there is even a suggestion to a wannabe Ph. D. for a thesis topic. (Removal of the "twice differentiable" hypothesis from one of the Schnirel'mann's theorem) There is a direct connection with this thread in this group as follows: The Schnirel'mann introduced a method which allows one to show that there is a number C with the property that any even number can be written as a sum of at most C primes. Goldbach conjecture states that C = 2. A question was raised as to the value of C that results from the Schnirel'mann's method. A number 300,000 appears in several places, but no one could come up with an exact reference to an honest calculation. The present article perpetuates the myth, in a way, it states that C is of the order of several hundreds of thousands, but no reference is given again.
The article also provides an interesting glimpse into the private lives of Soviet mathematicians: Luzin is alleged to have been a mystic, and Schnirel'mann himself committed suicide at the age of 33 because he expected to be arrested and questioned (tortured?) by NKVD (the precursor of the KGB).
The URL address is:
http://www.vdrobot.com/Handouts/SchnrlmnnUsenet.pdf
As ever,
Vlad
=================== * Vladimir Drobot * Retired and gainfully unemployed * http://www.vdrobot.com * mailto:drobot@pacbell.net ==================



