The quest for narrow admissible tuples

14 Jul

Secret Blogging Seminar

(A guest post by Andrew Sutherland.)

With more than 400 comments tacked on to the previous blog post, it’s past time to rollover to a new one. As just punishment for having contributed more than my fair share of those comments, Scott has asked me to write a guest post summarizing the current state of affairs. This task is made easier by Tao’s recent progress report on the polymath project to sharpen Zhang’s result on bounded gaps between primes. If you haven’t already read the progress report I encourage you to do so, but for the benefit of newcomers who would like to understand how our quest for narrow admissible tuples fits in the bounded prime gaps polymath project, here goes.

The Hardy-Littlewood prime tuples conjecture states that every admissible tuple has infinitely many translates that consist entirely of primes. Here a tuple is simply a set of…

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