Timeline for What can one say about $\sum\limits_{i=1}^\infty \frac{1}{p_{i+1}^2-p_i^2}$?
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| Apr 6, 2021 at 21:39 | comment | added | Sylvain JULIEN | Coming from Will, that's not unusual :-) | |
| Apr 6, 2021 at 21:38 | comment | added | Will Sawin | @YaakovBaruch Well, in addition I think it's pretty likely that sieve methods can give a proof the sum converges. I am trying to see if I can find a nice reference that helps with this. So you could wait to see if such a proof emerges... | |
| Apr 6, 2021 at 21:32 | comment | added | Yaakov Baruch | I hadn't heard of Cramer's conjecture before. Still I was guessing something similar and as a result was then using $\sum_{i=1}^{n} \frac{1}{ p_{i+1}^2 - p_i^2} + \frac{1}{2} \left( \frac{ \log \log p_{n+1} }{ \log p_{n+1} } \right) $ in my computation. Both your version and mine converge very very slowly, but it's probably as good as it gets... I'll wait until tomorrow to accept an answer, since yours came so lightening fast! | |
| Apr 6, 2021 at 21:24 | history | edited | Will Sawin | CC BY-SA 4.0 |
added 336 characters in body
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| Apr 6, 2021 at 21:17 | history | answered | Will Sawin | CC BY-SA 4.0 |