Timeline for Greatest number of coprime numbers between two numbers
Current License: CC BY-SA 3.0
16 events
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| Sep 23, 2015 at 20:09 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Sep 23, 2015 at 20:06 | comment | added | GH from MO | @Arul: See my added sections. | |
| Sep 23, 2015 at 20:04 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Sep 23, 2015 at 19:52 | comment | added | GH from MO | @PéterKomjáth: I added a brief summary of some relevant parts of the Erdős survey, thanks a lot for sharing it! | |
| Sep 23, 2015 at 19:50 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Sep 23, 2015 at 9:06 | comment | added | user76479 | @PéterKomjáth I cannot read hungarian, would it be possible to summarize results and asymptotics in a few sentences? | |
| Sep 23, 2015 at 8:47 | comment | added | Konstantinos Gaitanas | @Péter Komjáth Does the paper exist in English? | |
| Sep 23, 2015 at 6:53 | comment | added | Péter Komjáth | @GH from MO: renyi.hu/~p_erdos/1962-23.pdf | |
| Sep 23, 2015 at 5:54 | comment | added | GH from MO | @Arul: I guess by "number of coprimes integers in $[n,m]$" you mean "maximal size of a subset $S\subset[n,m]$ consisting of pairwise coprime integers". I don't think there will be a precise equation as you envision, but as I said all three terms will be very close to the actual prime count in the three given intervals, so the equation will hold up to a little error. Estimating the error precisely is a subtle problem in my opinion, and probably Erdős worked on this problem. | |
| Sep 23, 2015 at 5:50 | comment | added | user76479 | I am thinking following: Number of coprimes integers in $[n,m]$ = number between $[0,m]$ - number between $[0,n]$. Each term in difference follows PNT from your post? | |
| Sep 23, 2015 at 5:47 | comment | added | GH from MO | @Arul: For general intervals the size of such a subset might exceed the number of primes in the interval, e.g. $\{5,6,7\}$ vs. $\{5,7\}$, but probably by not too much. One can certainly estimate the size with the usual sieves, but I don't know the state of the art here. Something tells me Erdős worked on this problem, but I don't have time to think about this or check the literature. The general question is definitely more interesting. | |
| Sep 23, 2015 at 5:42 | vote | accept | CommunityBot | ||
| Sep 23, 2015 at 5:42 | comment | added | user76479 | I think from your answer it should be same. | |
| Sep 23, 2015 at 5:40 | comment | added | user76479 | Using PNT we can count number of primes between $m$ and $n$. Do we have roughly the same statistics for number of pairwise coprime numbers between $m$ and $n$ (this was what was in my mind)? | |
| Sep 23, 2015 at 5:38 | comment | added | user76479 | oops I meant an interval. I was looking at joro's post and forgot to update. | |
| Sep 23, 2015 at 5:37 | history | answered | GH from MO | CC BY-SA 3.0 |