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Goldbach conjecture
Conjecture Every even integer greater than 2 is the sum of two primes.
This famous conjecture is one of the oldest unsolved problems in mathematics. It arose originally out of a correspondence (1742) between Goldbach and Euler. See Wikipedia's Goldbach's conjecture for more.
Goldbach conjecture
On November 22nd, 2007 Benschop says:
Those interested in a suggestion for a proof via semigroup theory and carry extension, see: "Additive structure of Z(.) mod [\prod first k primes], with carry extension to prime pair sums". - http://home.iae.nl/users/benschop/ngb0203.pdf (10 pgs, submitted for publication)
Goldbach conjecture
On December 12th, 2007 Anonymous says:
In addition to the above link to the paper with Goldbach-Conj. proof, the abstract and links to an intro-article are at http://home.iae.nl/users/benschop/ng-abstr.htm
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CSI of Charles University
Weak conjecture now solved
Note that Harald Helfgott has proved the ternary version of Goldbach's conjecture, that every odd number greater than 7 is the sum of three odd primes. See http://arxiv.org/abs/1205.5252 (minor arc estimates) and http://arxiv.org/abs/1305.2897 (major arc estimates).