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

 Messages: [ Previous | Next ]
 drobotv@gmail.com Posts: 14 Registered: 5/21/07
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. 2-6. 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).

http://www.vdrobot.com/Handouts/SchnrlmnnUsenet.pdf

As ever,

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Date Subject Author
1/15/10 Matthew Watkins
1/15/10 Olivier
1/17/10 Matthew Watkins
1/17/10 markvs@gmail.com
1/19/10 Olivier
1/19/10 drobotv@gmail.com
1/25/10 drobotv@gmail.com
1/26/10 Heine Rasmussen
1/28/10 JEMebius
3/1/10 drobotv@gmail.com
1/20/10 tchow@lsa.umich.edu
1/23/10 Matthew Watkins