From: sfinch@mathsoft.com Newsgroups: sci.math Subject: Re: Question: What's the latest in Goldbach's Conjecture ? Date: Wed, 23 Dec 1998 18:50:37 GMT Hello! The latest progress is briefly summarized at http://www.mathsoft.com/asolve/constant/hrdyltl/goldbach.html The ternary version of Goldbach's conjecture has been solved, subject to the truth of a generalized Riemann hypothesis. The proof of this, due to J.-M. Deshouillers, G. Effinger, H. te Riele and D. Zinoviev, is at http://www.ams.org/era/home-1997.html Steve Finch In article <3680B04D.36394A03@vlsi.informatik.tu-darmstadt.de>, Oliver Hauck wrote: >... > can anybody help me in giving pointers to recent papers concerning > Goldbach Conjecture ? >... -----------== Posted via Deja News, The Discussion Network ==---------- http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own ============================================================================== From: "Hub-R-ISS-1" Newsgroups: sci.math Subject: Re: Goldbach Date: Sun, 3 Jan 1999 23:39:59 +1100 Wang Yong wrote in message <01be370a$c9a83fc0$0d44bd89@PC001.econ.cuhk.edu.hk>... >Can someone confirm what the Goldbach conjecture says: Does it say "an even >number" or "any non-prime number", that can be decomposed into the sum of >two primes? By the way, does anyone know what is the status regarding this >conjecture as of now? 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? > >Thanks, > >Yung Wong > The current status on the Goldbach conjecture, according to http://www.mathsoft.com/asolve/constant/hrdyltl/goldbach.html (which of course doesn't mean it's gospel, but I believe it) is as follows: It has been proven that every odd number is the sum of three primes. It has been proven that every even number is the sum of no more than six primes. It has been proven that every sufficiently large even number is the sum of a prime and a number with no more than 2 prime factors. Hope Hubris Tyrant of Jupiter ============================================================================== Remarks: 1. The number of representation of 2n as a sum of two primes generally increases with n, so it's rather frustrating not to be able to prove that this number is at least 1 ! 2. From time to time one encounters numbers 2n for which 2n-p is composite for all small primes p. Here are the values of 2n for which "record" numbers of small primes must be tested. (That is, if f(2n)=min{p; p and 2n-p are prime} then f(2n) > f(2k) for all k < n.) [2n,f(2n)]=[6, 3], [12, 5], [30, 7], [98, 19], [220, 23], [308, 31], [556, 47], [992, 73], [2642, 103], [5372, 139], [7426, 173], [43532, 211], [54244, 233], [63274, 293], [113672,313], [128168,331], [194428,359], [194470,383], [413572,389], [503222,523], [1077422,601], [3526958,727], [3807404,751], [10759922,829], ... Additional values of 2n form sequence A025018 in Sloane's sequence server.