Timeline for Upper bound for the number of $k$-central numbers in a prime gap
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 2, 2021 at 15:12 | comment | added | Sylvain JULIEN | And indeed GC alone may not be strong enough, we probably need what I call NFPR conjecture in the link I gave. | |
| Mar 2, 2021 at 15:10 | comment | added | Wojowu | Goldbach conjecture doesn't guarantee anything beyond $l(n)=O(n)$. True order of growth is probably smaller but we would need stronger assumptions to prove that. | |
| Mar 2, 2021 at 15:07 | comment | added | Sylvain JULIEN | I expect something along the lines of $l(n)=O(\log^{\alpha}p_{n})$ for some $\alpha>1$ but that may sound a bit too optimistic. | |
| Mar 2, 2021 at 14:55 | comment | added | Wojowu | I have no idea what relation whatsoever to Cramer's conjecture this bears. If you are intending to use the bound in terms of $l(n)$ you propose, then I doubt it given there is no way to derive any nontrivial bounds from Goldbach conjecture. | |
| Mar 2, 2021 at 14:32 | comment | added | Sylvain JULIEN | Can we thus get somewhat closer to Cramer's conjecture? | |
| Mar 2, 2021 at 14:24 | comment | added | Sylvain JULIEN | That's merely astonishing. I didn't quite get your argument, but I'll get back to it later. Thanks a lot! | |
| Mar 2, 2021 at 14:21 | vote | accept | Sylvain JULIEN | ||
| Mar 2, 2021 at 12:57 | comment | added | Wojowu | Assuming the prime tuple conjecture, the bound $N_{I_n}(k)\leq k$ will also be optimal for every $k$. I doubt an unconditional proof is possible here though. | |
| Mar 2, 2021 at 12:49 | history | answered | Wojowu | CC BY-SA 4.0 |