Timeline for Primes isolated by large gaps to either side
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20, 2015 at 9:38 | vote | accept | Joseph O'Rourke | ||
| Apr 19, 2015 at 21:53 | comment | added | GH from MO | @GerhardPaseman: Indeed, your version of the inequality is not known to hold for infinitely many $n$'s when $k=1$, but it is known to hold when $k<1$. | |
| Apr 19, 2015 at 20:42 | comment | added | Gerhard Paseman | It would seem that what is known falls short of $p_{n+1} - p_n \gt \log p_n(\log(\log p_n))^k$ being true for fixed $k \geq 1$ and infinitely many $n$. (I think that) Joseph and I would appreciate if you can confirm/deny this assertion, especially the $k \geq 1$ part. Gerhard "Lost In Number Theory Lumberyard" Paseman, 2015.04.19 | |
| Apr 19, 2015 at 19:33 | comment | added | GH from MO | @TheMaskedAvenger: Thanks for the clarification. I think this writeup has not appeared, but I have no doubt it will. The way I interpret the authors' remark is as follows: given any $m>1$, there are infinitely many $n$'s so that the minimal gap size between the primes $p_n,\dots,p_{n+m}$ is significantly larger than $\log n$, perhaps as large as the bound in Theorem 1 of the paper (corresponding to $m=1$). The matrix method will play a role in the proof of this result. | |
| Apr 19, 2015 at 19:10 | comment | added | The Masked Avenger | On rereading my comment, "hint at an answer" seems overly strong, and "make significant progress" seems more appropriate. I'm sorry if I misled you. | |
| Apr 19, 2015 at 19:02 | comment | added | The Masked Avenger | No, but between Theorem 1 and the section 1.1 they cite a sequel which extends the Maier matrix method. I may be misreading things, so I ask you, since you seem more able with the analytic number theory literature (compared to me, which isn't saying much). | |
| Apr 19, 2015 at 17:16 | comment | added | GH from MO | @TheMaskedAvenger: Can you be more specific, with exact page and line number in the document arxiv.org/pdf/1412.5029v2.pdf ? | |
| Apr 19, 2015 at 16:25 | comment | added | The Masked Avenger | In the document behind your link, they hint at an answer to Joseph's question. Do you know if that writeup has appeared, even in prearxiv form? | |
| Apr 19, 2015 at 16:20 | history | answered | GH from MO | CC BY-SA 3.0 |