Unless listed below, all the above bounds were produced by the Polymath8 project. [BI]: R. C. Baker, A. J. Irving, Bounded intervals containing many primes [M]: J. Maynard, Small gaps between primes We have been working on improving a number of other quantities, including the quantity [math]H_m[/math] mentioned above: [math]H = H_1[/math] is a quantity such that there are infinitely many pairs of