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]\displaystyle{ H_m }[/math] mentioned above: [math]\displaystyle{ H = H_1 }[/math] is a quantity such that t