Timeline for Consequences of Legendre's conjecture
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 25, 2018 at 15:18 | history | protected | YCor | ||
| Aug 15, 2014 at 20:49 | comment | added | user57176 | I think we should look at the upper bound of total number of composite integers in the interval .That should facilitate the solution in my view. | |
| Feb 26, 2013 at 1:58 | answer | added | Andrew Granville | timeline score: 21 | |
| Feb 14, 2013 at 11:08 | vote | accept | Nirakar Neo | ||
| Feb 9, 2013 at 14:59 | answer | added | user9072 | timeline score: 7 | |
| Nov 27, 2012 at 16:47 | comment | added | Nirakar Neo | Oh. I see. Thank you for the explanation. So basically it is equivalent to the some mentioned gap between consecutive primes. You may close the question if you wish. | |
| Nov 27, 2012 at 9:47 | comment | added | user9072 | Conversely if you knew the gap between consecutive primes was always at most $2 \sqrt{p} + 1$ you would get LC. To repeat my point: LC todays seems like quite an arbitrary conjectue; very very likely it is true since much stronger things are believed to be true. See here en.wikipedia.org/wiki/Prime_gap | |
| Nov 27, 2012 at 9:38 | comment | added | user9072 | Are you looking on literature on gaps between primes or consequence of Legendre's conjecture? I mean Legendre's conjecture implies a bound on gaps between primes, is direct, indeed IMO it essentially is a conjecture on gaps between primes, or primes in short intervals, stated in an (by nowadays standards) unnatural way, which is my point: What is the worst case for two consecutive primes $p,q$ if LC is true $n^2$ and $(n+2)^2$ (well one could save a bot but let us ignore this). So the difference is max $4n + 4$ and $\sqrt{p}$ being at least $n$ you get a bound of $4\sqrt{p} + 4$ for $q-p$. | |
| Nov 26, 2012 at 8:45 | comment | added | Nirakar Neo | May be it's now of historical value, but still it's unsolved. I was discussing with my friend on its implications. On the wiki, we just found that its truth allows to have stricter bound on gaps of primes (as mentioned at the wikipedia page). So I was looking if there is some literature on this. | |
| Nov 26, 2012 at 6:23 | comment | added | Alexander Chervov | may be interesting to look at KConrad answer mathoverflow.net/questions/17209/… Item c) briefly discusses Legendre conjecture and GRH, etc. | |
| Nov 25, 2012 at 8:51 | comment | added | user9072 | Since in my opinion Legendre's conjecture is mainly of historical value, as opposed to having in itself a proper prominent place in current research, the motivation for this seems unclear. Voting to close. | |
| Nov 25, 2012 at 7:20 | history | asked | Nirakar Neo | CC BY-SA 3.0 |