1
$\begingroup$

Let $d$ be the least positive integer such that there are infinitely many distinct prime pairs $\{p,q\}$ with $|q-p|\le d$. The twin prime conjecture is equivalent to $d=2$. In 2013 Yitang Zhang proved that $d\le 7\times10^7$. Maynard improved this to $d\le600$, and a Polymath Team led by Tao obtained further that $d\le 246$.

Quite recently, Chunlei Liu released a prperint On the gap between primes in which he modified Maynard's approach to get $d\le 130$.

Question. What's the advantage in Liu's modification of Maynard's method? Can Liu's work be improved further? Can one prove $d<130$ via suitable refinements?

I have not read Liu's paper very carefully. Your helpful comments are welcome!

Improve this question
$\endgroup$
4
  • 11
    $\begingroup$ The first version of this preprint claimed $d\leq 20$, then it increased to 90, got down to 26, then up to 130. I would wait a little before taking any conclusion. $\endgroup$
    – abx
    Commented Mar 20, 2022 at 7:37
  • $\begingroup$ I'm curious generally how much effort has gone into improving $246$, even to $245$, say. $\endgroup$
    – mathworker21
    Commented Mar 20, 2022 at 11:44
  • 5
    $\begingroup$ See the following MO thread for certain bottlenecks in improving 246: mathoverflow.net/questions/392178/… $\endgroup$
    – Ofir Gorodetsky
    Commented Mar 20, 2022 at 12:14
  • 2
    $\begingroup$ 12 versions of an arxiv preprint claiming big progress on a big conjecture isn't a sign of hope.... $\endgroup$
    – David Roberts ♦
    Commented Mar 20, 2022 at 20:20

0

Reset to default

You must log in to answer this question.