Timeline for Is there always a prime between $\beta z^\alpha$ and $\beta (z+1)^\alpha$ for $z$ large enough, and a fixed $\alpha < 2$?
Current License: CC BY-SA 4.0
5 events
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| Jun 22, 2020 at 13:48 | comment | added | Vincent Granville | Thank you. I guess I will stop wasting my time trying to prove my problem. That was supposed to be the easiest of the two big challenges I am facing, and it turns out to be unproven yet. | |
| Jun 22, 2020 at 9:33 | comment | added | Wojowu | Correction from my previous comment: the exponent should be, I think, $\frac{\alpha-1}{\alpha}$, not $\alpha-1$. | |
| Jun 22, 2020 at 7:27 | comment | added | Gerry Myerson | Indeed, it's not even known whether there's always a prime between consecutive squares, so the question here seems hopeless. | |
| Jun 21, 2020 at 23:33 | comment | added | Wojowu | Of course, the answer is "no" for $\alpha\leq 1$. For $\alpha>1$ this is conjecturally true, but not proven. This is a question about maximal prime gaps, specifically whether they are $O(p_n^{\alpha-1})$. See here for known results. | |
| Jun 21, 2020 at 23:28 | history | asked | Vincent Granville | CC BY-SA 4.0 |