Timeline for What is the minimal range $[f(n),g(n)]$ that contains a prime number for every integer $n>0$?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 1, 2014 at 22:56 | vote | accept | barak manos | ||
| Feb 27, 2014 at 14:46 | comment | added | GH from MO | @barak: The "$n$-th prime number" has a short formal definition within set theory (ZFC), it is a translation of the usual definition "in words". In fact any recursive function can be represented by a first order formula within Peano arithmetic. | |
| Feb 27, 2014 at 12:15 | comment | added | barak manos | @GH from MO: Well I kinda meant mathematical symbols (though I'm not sure how to express this meaning in a "mathematical notion"). | |
| Feb 27, 2014 at 10:46 | comment | added | GH from MO | It is easy to define $P_n$ with a few symbols: $P_n$ is the $n$-th prime number. | |
| Feb 27, 2014 at 10:25 | comment | added | barak manos | @Pietro Majer, thanks... either way, what I meant is a range between two "finitely defined" functions $f(n)$ and $g(n)$. Can you define $P_n$ in a finite "amount of paper"? | |
| Feb 27, 2014 at 10:23 | comment | added | Pietro Majer | Actually I really meant $f(n)=g(n)=p_n$. | |
| Feb 27, 2014 at 9:04 | comment | added | barak manos | @Pietro Majer: Oh, I understand now, you mean $f(n)=P_{n}$ and $g(n)=P_{n+1}$? | |
| Feb 27, 2014 at 9:00 | comment | added | Pietro Majer | Then maybe your problem is : the function $f$ being ${\it given}$, ${\it find}$ the smallest function $g\ge f$ such that there is a prime in the interval? I was just saying that if we can choose both $f$ and $g$ there is the trivial answer above. | |
| Feb 27, 2014 at 8:55 | comment | added | barak manos | It will not describe my question properly if I do so. Please note that I'm asking if there is a prime number between $n^2$ and $(n+1)^2$. How can $f(n)$ be $n$ in this case? | |
| Feb 27, 2014 at 8:53 | comment | added | Pietro Majer | I think it is more clear if you fix $f$ to be the identity, $f(n)=n$ (besides, taking $f(n)=g(n)=p_n$ would somehow trivialize the question) | |
| Feb 27, 2014 at 8:43 | answer | added | user9072 | timeline score: 6 | |
| Feb 27, 2014 at 8:25 | answer | added | GH from MO | timeline score: 7 | |
| Feb 27, 2014 at 8:04 | history | edited | barak manos | CC BY-SA 3.0 |
added 392 characters in body
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| Feb 27, 2014 at 7:58 | history | asked | barak manos | CC BY-SA 3.0 |