Fred, Thanks for this. However, their work is for approximations to the twin prime conjecture. It doesn't say anything about Goldbach. Victor On Wed, Nov 20, 2013 at 9:46 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Since this topic has subsided from public view, a priesthood incorporating James Maynard, Andrew Granville, Terry Tao, has been assiduousy shaving Zhang's original 70 million, and refining and simplifying the proof to the point where a normal mathematically-inclined human (if such an entity exists) might possibly be able to follow it with the assistance of a powerful computer and a sabbatical year or two --- by which time it would no doubt have undergone further drastic improvement.
The current result asserts that there are infinitely many consecutive prime pairs with difference h for some h <= 600 . The result generalises to finite arithmetic progressions of m consecutive primes with span h , for which instead h <= exp(8m + 5) .
For those with time to spare and robust self-esteem, there is (considerably) more detail available at
http://terrytao.wordpress.com/2013/11/19/polymath8b-bounded-intervals-with-m...
Fred Lunnon
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