In this 1998 journal paper, all the prime knots with 16 or fewer crossings are found (some of which were found earlier by others). There are over 1.7 million such knots. But the prime knots with 17 crossings have not yet been tabulated. Here is what this book says:

This is probably hard and requires new ideas.

But this book was written in 2004, so things may have changed since then. There have certainly been a lot of developments in knot theory over the past 15 years.

So my question is, what is the state of research on finding all prime knots with 17 crossings? Are we relatively close to doing so, and have partial results been discovered?


Ben Burton has found that there are 352,152,252 prime non-trivial knots with up to 19 crossings. See here for the tables.

  • $\begingroup$ Why isn’t this major news? Why hasn’t this result been published in journals? $\endgroup$ Sep 12 '19 at 20:26
  • $\begingroup$ I believe it is currently being written up. I saw him give a talk about this result at a recent conference. $\endgroup$
    – Josh Howie
    Sep 12 '19 at 20:43
  • 2
    $\begingroup$ It does say on that page that the paper would appear on arXiv in June 2018, so what happened? $\endgroup$
    – liuyao
    Sep 12 '19 at 20:47
  • 2
    $\begingroup$ Things sometimes take longer than expected, as I'm sure every mathematician has experienced first-hand. If the precise details matter to you, you can of course e-mail Ben. $\endgroup$
    – mme
    Sep 12 '19 at 21:50
  • 2
    $\begingroup$ If you think a one year lag on a paper is unusual, you must be young. I've got a pre-print that I've been getting ready for publication for the past 11 years... $\endgroup$ Sep 13 '19 at 3:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.