From: bobs@rsa.com
Subject: Re: Goldbach
Date: Mon, 04 Jan 1999 16:08:38 GMT
Newsgroups: sci.math
Keywords: Goldbach conjecture
In article <76no12$df6$1@phys-ma.sol.co.uk>,
"Robert Harrison" wrote:
>
> Wang Yong wrote in message
> <01be370a$c9a83fc0$0d44bd89@PC001.econ.cuhk.edu.hk>...
> >....Also, I remember that the Chinese mathematian Chen
> >Jiang-run proved long time ago something referred as "1+2". Anyone know
> >what is this "1+2", and the exact reference to the publication of this
> >result?
> Chen proved that every even integer can be expressed as the sum of a prime
> and a composite of 2 primes. I believe details can be found in Sieve Methods
> by Halberstam and Richert, Academic Press, London, 1974.
Not quite. Chen proved that every even integer is the sum of a prime and
a number with AT MOST two prime factors. To prove EXACTLY two prime
factors would probably require solving the parity problem.
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==============================================================================
From: jpr2718@aol.com (Jpr2718)
Subject: Re: GoldBach's Conjecture
Date: 22 Mar 1999 00:46:00 GMT
Newsgroups: sci.math
The question as to whether every even number at least 6 is a sum of two odd
primes remains open.
Vinogradov showed (in 1937) that every odd number greater than 3^(3^15) is the
sum of three primes, and Chen Jing-Run and Wang Tian-Ze reduced this to
e^(e^11.503) in 1989.
Chen (1973) showed that all large enough numbers are the sum of a prime and a
number that is either a prime or the product of two primes.
See http://www.utm.edu/research/primes/glossary/GoldbachConjecture.html and
related links for more information.
John
==============================================================================
From: gerry@mpce.mq.edu.au (Gerry Myerson)
Subject: Re: GoldBach's Conjecture
Date: Tue, 23 Mar 1999 15:43:30 +1100
Newsgroups: sci.math
In article <19990321194600.07015.00000243@ng-fa1.aol.com>, jpr2718@aol.com
(Jpr2718) wrote:
> Vinogradov showed (in 1937) that every odd number greater than 3^(3^15) is the
> sum of three primes, and Chen Jing-Run and Wang Tian-Ze reduced this to
> e^(e^11.503) in 1989.
More recently, Deshouillers, Effinger, te Riele, and Zinoviev proved that
if the Riemann Hypothesis holds, then every odd number greater than 5 is
a sum of three primes. RH somehow allows you to bring the Vinogradov et al
bounds down to where a computer can finish things off.
The cynical point of view is that this is not helpful, since we were already
certain about the conclusion, while we remain doubtful about the hypothesis.
Gerry Myerson (gerry@mpce.mq.edu.au)
==============================================================================
From: Kurt Foster
Subject: Re: Goldbach Conjecture
Date: 25 Apr 1999 15:42:44 GMT
Newsgroups: sci.math
In <7fub2r$k3o$1@imsp009a.netvigator.com>, Anthony said:
. I would like to find some information about the proof of the Goldbach
. Conjecture, especially the proof made by the chinese mathematician
. Mr.Chen.
Chen didn't prove the conjecture, but he did come tantalizingly close:
every "sufficiently large" even number is of the form P + P2, where P is
prime and P2 is at most the product of two primes. Unfortunately, the
method used doesn't admit determination of how large is "large enough."
See the book "Sieve Methods" by Halberstam and Richert for a proof of
Chen's result.
==============================================================================
From: Andreas Homrighausen
Subject: Re: Unsolved Theorems or Thories?
Date: Fri, 12 Feb 1999 15:01:39 +0100
Newsgroups: sci.math
Jeremy Lee wrote:
>
> correct me if I'm wrong, but I seem to remember something called
> "Goldbach's Conjecture" which is that every integer >2 can be
Every even(!) number greater than 4 can be written as the sum
of two odd primes...
Goldbach wrote a letter to Euler in which he stated his conjecture.
Here you can find it:
http://www.informatik.uni-giessen.de/staff/richstein/de/goldbach.jpg
Greetings,
Andreas