The (presumably) final article arising from the Polymath8 project has now been uploaded to the arXiv as “The “bounded gaps between primes” Polymath project – a retrospective“. This article, submitted to the Newsletter of the European Mathematical Society, consists of personal contributions from ten different participants (at varying levels of stage of career, and intensity of participation) on their own experiences with the project, and some thoughts as to what lessons to draw for any subsequent Polymath projects. (At present, I do not know of any such projects being proposed, but from recent experience I would imagine that some opportunity suitable for a Polymath approach will present itself at some point in the near future.)
This post will also serve as the latest (and probably last) of the Polymath8 threads (rolling over this previous post), to wrap up any remaining discussion about any aspect of this project.
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31 October, 2016 at 12:22 pm
Anonymous
Note that if
are primes greater than 
, it is easy to verify that 
and 
, which implies your observation that 
is divisible by 
.
1 November, 2016 at 10:41 am
Sultan M.
I am very thankful for your clear explaination
30 April, 2019 at 10:57 am
Terence Tao
As this project has been inactive for many years it is perhaps unlikely that too many of the former participants are still following this thread. Nevertheless, this seems like the right place to make a small announcement: I have been informed that the Polymath8b paper “Variants of the Selberg Sieve, and bounded intervals containing many primes” published in Research in the Mathematical Sciences was just selected for the inaugural “Best Paper Award” by that journal (an official announcement of this shall be made shortly). This award comes with a modest cash prize ($500) which obviously cannot be accepted by the pseudonymic DHJ Polymath. However, they can donate this prize to some charitable cause instead. The editor at RMS handling the paper, Ken Ono, suggested donating to the AMS “Who wants to be a mathematician?” contest; other suggestions are welcome.
30 April, 2019 at 2:39 pm
Robert Silverman Silverman
What about the Number Theory Foundation? Established by John Selfridge, I believe.
Number Theory Foundation
Department of Mathematics
Dartmouth College
Hanover, NH 03755
30 April, 2019 at 3:49 pm
Anonymous
I think this is a good idea. The number theory foundation is likely to support the kind of mathematics that was related to this Polymath project.
7 May, 2019 at 10:25 am
Terence Tao
This sounds like a very appropriate use of the funds, especially since the NTF nowadays is primarily sponsoring a best paper award of its own (the Selfridge prize). I will let RMS know that this is where we would like the prize funds to be directed.
12 February, 2020 at 6:33 pm
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22 April, 2020 at 9:52 am
Andrew Sutherland
This is a quick update for anyone still interested in the Polymath8 admissible tuples database, which stores the best upper bounds on H(k) we have for k up to 5000, along with an admissible tuple that achieves this bound. The company that was hosting this database was recently acquired and the new owner no longer offers a zero-cost hosting option. I moved the database to a static DataTable that you can browse and search at https://math.mit.edu/~primegaps (JavaScript required).
Using static tables means we can no longer easily accept online submissions, but if anyone manages to improve a tuple, feel free to email me and I can update the database manually.
p.s. On an unrelated note, I am happy to report that the Number Theory Foundation is back in business. The link Terry posted on 7 May 2019 used to lead to a notice that the NTF planned to fund only the Selfridge Prize going forward, but this is no longer true; if you click on the link in Terry’s Post you will find yourself redirected to our new web site.