Timeline for A result on prime numbers [closed]
Current License: CC BY-SA 2.5
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2010 at 6:38 | vote | accept | Roupam Ghosh | ||
| Jan 2, 2010 at 1:03 | vote | accept | Roupam Ghosh | ||
| Jan 21, 2010 at 6:38 | |||||
| Jan 1, 2010 at 21:12 | history | closed | Anton Geraschenko | not a real question | |
| Jan 1, 2010 at 21:12 | comment | added | Anton Geraschenko | It's fine to ask, "are these results known and does somebody have a reference?" But this has turned into a game of "debug my proof for me," which (in this form at least) is not appropriate for Math Overflow. I'm closing the question (direct discussion about it to tea.mathoverflow.net/discussion/124). If the question is edited to sharpen it (i.e. make it a question that has an answer), or if somebody otherwise convinces me (or another moderator, or five 3k+ rep users), the question can be reopened. | |
| Jan 1, 2010 at 19:50 | answer | added | maki | timeline score: 0 | |
| Jan 1, 2010 at 19:11 | comment | added | Leonid Positselski | @rpg: your first implication is not justified. This is called "1 to the power \infty", a kind of expression whose limit you cannot know just from knowing the limits of the constitutient subexpressions. You are repeating your original mistake here, in a slightly disguised form. | |
| Jan 1, 2010 at 19:04 | comment | added | Leonid Positselski | @Ilya: I did as you requested. | |
| Jan 1, 2010 at 18:59 | answer | added | Leonid Positselski | timeline score: 6 | |
| Jan 1, 2010 at 18:51 | comment | added | Roupam Ghosh | but leonid, you struck a great point there... here are my thoughts on it... lim inf p(n+1)/p(n) = 1 implies lim inf (p(n+1)/p(n))^p(n) = 1 implies lim inf log((p(n+1)/p(n))^p(n)) = 0 implies lim inf p(n)log(p(n+1)/p(n)) = 0 Does this resolve it? | |
| Jan 1, 2010 at 18:40 | comment | added | Roupam Ghosh | @leonid: yea... sorry for that... but anyways, i am not using PNT for that equation, just tried to give an idea, but damn!!! | |
| Jan 1, 2010 at 18:35 | comment | added | Leonid Positselski | The limit you write now is equal to 1 and not to 0. (Neither does the second equation sign in your formula seem to be justified from PNT.) | |
| Jan 1, 2010 at 18:21 | comment | added | Roupam Ghosh | Well, i didnt want to actually apply the PNT... but just to give an idea, then it would have looked like \begin{equation} \begin{split} \lim \inf_{n\to\infty} \frac{d_n}{\log p_n} & = \lim \inf_{n\to\infty} \frac{p_n}{\log p_n} \log \left( \frac{p_{n+1}}{p_n} \right)\\ & = \lim \inf_{n\to\infty} \frac{\log n}{\log n + \log \log n} \log \left( 1 + 1/n \right)^n\\ & = 0 \end{split} \end{equation} | |
| Jan 1, 2010 at 18:17 | comment | added | Ilya Nikokoshev | @Leonid, I think you're right and you should post your observation as an answer -- it could be accepted then. | |
| Jan 1, 2010 at 17:20 | comment | added | Leonid Positselski | I am no specialist in analytic number theory, but from what I know from analysis the limit computation (10) is clearly wrong. You have the product of two factors, the first (p_n/log p_n) of which goes to infinity and the second goes to zero, and so it does not follow that the product goes to zero. | |
| Jan 1, 2010 at 16:44 | comment | added | Roupam Ghosh | Thanks for the good news!!! But that actually made me more skeptical... because in maths mostly, "easy implies wrong"... and if there are any errors... I'd love to debug them, now that I know the problem is so important :D I have posted my paper here: arxiv.org/pdf/0912.4646 Would love to get comments... | |
| Jan 1, 2010 at 15:52 | comment | added | fedja | The other two claims can easily be derived from known power bounds on prime gaps, but still, it would be interesting to see how you do them. So, yes, this is high quality work (provided it is correct, of course). | |
| Jan 1, 2010 at 15:26 | comment | added | Thomas Bloom | First result, that is. | |
| Jan 1, 2010 at 15:26 | comment | added | Thomas Bloom | Your result is due to Goldston and Yildirim, and was only established in the last 10 years, using sophisticated sieve theory techniques. It would be very impressive if you had found an easy/elementary proof of this. | |
| Jan 1, 2010 at 15:20 | history | asked | Roupam Ghosh | CC BY-SA 2.5 |