Yitang Zhang’s very recent shocking paper demonstrated that bounded gaps between primes occur infinitely often, with the explicit upper bound of 70,000,000 given for this gap. Polymath8 was launched for the dual purpose of learning Zhang’s proof and improving the upper bound for the gaps. Here are links for three posts (I, II, III) on Terry Tao’s blog, a post on the secret blogging seminar, and for a post on the polymath blog. And here is the table for the world records so far.

**Updates:** Record for June 16 – **60,744**

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