Timeline for Does always exist a prime number between $n(n+1)$ and $(n+1)(n+2)$?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 3, 2023 at 16:25 | comment | added | Terry Tao | See also the marginally stronger conjecture of Oppermann: en.wikipedia.org/wiki/Oppermann%27s_conjecture | |
| Oct 3, 2023 at 14:55 | answer | added | G. Melfi | timeline score: 2 | |
| Jun 17, 2021 at 4:23 | answer | added | 2734364041 | timeline score: 10 | |
| Jun 15, 2021 at 11:56 | review | Close votes | |||
| Jun 17, 2021 at 16:47 | |||||
| Jun 15, 2021 at 8:00 | comment | added | Sylvain JULIEN | It is likely, that, letting $\Delta_{n}:=(n+1)(n+2)-n(n+1)$, one should have $\pi((n+1)(n+2))-\pi(n(n+1))>(1+o(1))\frac{\pi(\Delta_{n})^{2}}{\Delta_{n}}$. | |
| Jun 15, 2021 at 2:28 | comment | added | GH from MO | It is suspected, but far from being proven. | |
| Jun 15, 2021 at 2:07 | comment | added | John Omielan | The difference between $n(n+1)$ and $(n+1)(n+2)$ is $2(n+1) = 2n + 2$. Also, $n(n+1)$ is $n$ larger than $n^2$, plus $(n+1)(n+2) = n^2 + 3n + 2$ is $n + 1$ larger than $(n+1)^2$. Thus, what you're asking is very similar to Legendre's conjecture and, as such, I suspect it's also currently unknown. | |
| Jun 15, 2021 at 1:59 | history | asked | Đào Thanh Oai | CC BY-SA 4.0 |