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Small gaps between large gaps between primes results

The big news last year was the quest to find a lower bound for the gap between pairs of large primes, started by Yitang Zhang and carried on chiefly by Terry Tao and the fresh-faced James Maynard.

Now that progress on the twin prime conjecture has slowed down, they’ve both turned their attentions toward the opposite question: what’s the biggest gap between subsequent small primes?

Prime gaps update

There’s been some progress on the bounded gaps between primes front since we last checked in.

The Polymath8 project has got the gap down to $4,680$. But that’s small beans: James Maynard, a postgrad student at Oxford, announced at a meeting in Oberwolfach that he has got the gap down to $700$. Emmanuel Kowalski has written an effusive post on his blog singing the praises of Maynard’s achievement.