Timeline for Does always exist a prime number between $n(n+1)$ and $(n+1)(n+2)$?
Current License: CC BY-SA 4.0
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| Jun 17, 2021 at 17:20 | history | edited | 2734364041 | CC BY-SA 4.0 |
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| Jun 17, 2021 at 17:18 | comment | added | 2734364041 | @GHfromMO Good point...I should've caught that. I'll adjust my answer. | |
| Jun 17, 2021 at 15:11 | comment | added | GH from MO | Yes, same for Legendre's problem. We don't even know that, for large $x$, there always exists a prime in $[x,x+x^{0.501}]$, which is much weaker than either of the two conjectures. | |
| Jun 17, 2021 at 13:13 | comment | added | 2734364041 | @GHfromMO So the same would hold for Legendre's problem? I didn't realize that so little was known! | |
| Jun 17, 2021 at 7:42 | comment | added | GH from MO | We don't know that a threshold exists for the OP's question. That is, currently we cannot exclude the possibility that infinitely many counterexamples $n$ exist. | |
| Jun 17, 2021 at 4:48 | history | edited | 2734364041 | CC BY-SA 4.0 |
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| Jun 17, 2021 at 4:23 | history | answered | 2734364041 | CC BY-SA 4.0 |