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).
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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).