Thread: Prime Gap News
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Old 2021-09-09, 20:15   #262
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Dec 2008
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It is proven that there are infinitely prime pairs whose difference is no greater than 20.

I'm not quite convinced yet, even if I only understand rather little of the paper. Especially, on page 3, the set H = {0, 2, 6, 8, 12, 14, 18, 20} is not admissible. Omit the 14, then it works.
Achieving the result quoted without Elliott-Halberstamm or something similar would be quite big news. Any thoughts?
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