Timeline for What can one say about $\sum\limits_{i=1}^\infty \frac{1}{p_{i+1}^2-p_i^2}$?
Current License: CC BY-SA 4.0
11 events
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| Apr 14, 2021 at 15:28 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
Removed \displaystyle from the title
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| Apr 8, 2021 at 21:30 | comment | added | Yaakov Baruch | With $p_n$ close to $600\times 10^6$ and some (questionable) extrapolation, I now see a limit close to 0.633 (form either side). | |
| Apr 7, 2021 at 20:00 | vote | accept | Yaakov Baruch | ||
| Apr 7, 2021 at 9:13 | history | edited | GH from MO |
edited tags
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| Apr 7, 2021 at 0:40 | answer | added | Zhou | timeline score: 17 | |
| Apr 6, 2021 at 21:17 | answer | added | Will Sawin | timeline score: 4 | |
| Apr 6, 2021 at 21:14 | comment | added | Yaakov Baruch | @WillSawin. Yes, that is how I got the 0.63. But I may have messed up in the guessing the probabilistic large $n$ behavior. | |
| Apr 6, 2021 at 21:07 | comment | added | Wojowu | The question boils down to showing that small prime gaps are not frequent. For instance, I believe it would be sufficient to show that, for some $c,d>0$, there are $O(\frac{n}{(\log n)^c})$ prime gaps below $p_n$ which are smaller than $(\log n)^d$. This is certainly plausible from the conjectures on density of prime gaps, but I'm not sure whether results have been proven with suitable uniformity. | |
| Apr 6, 2021 at 21:07 | comment | added | Will Sawin | To compute a few digits, surely what you'd want to do is compute the first terms of the sum from primes $<N$ and then give a probabilistic model for the large $n$ behavior and integrate the expectation from $n=N$ to $\infty$? So it would be a combination of numerical data and heuristics to compute the digits. | |
| Apr 6, 2021 at 20:54 | history | edited | Yaakov Baruch | CC BY-SA 4.0 |
deleted 1 character in body
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| Apr 6, 2021 at 20:47 | history | asked | Yaakov Baruch | CC BY-SA 4.0 |