$2$ is the $1$st prime.  $3$ is the $2$nd prime.  $5$ is the $3$rd prime.  $11$ is the $5$th prime.  $31$ is the $11$th prime.  ...  I'm just wondering if there is a name for this integer sequence, is it on ?. I find it hard to find a suitable search term for it.
$127$ has an interesting property: It is the $31$st prime number and its rank ($31$) is also a prime. $31$ is the $11$th prime so its rank is also a prime. $11$ is also a prime number with a rank ($5$) that is also a prime. $5$ is the 3rd prime number and and so its rank ($3$) is also a prime. And finally $3$ is the $2$nd prime so its rank is also a prime... Is there a name for primes whose rank (index in the prime series) is also a prime? That is:     If $a_i$ is the $i$th prime number, then $i$ is a also a prime.   How about numbers like $127$ where going down ranks of ranks always produce prime numbers (down to rank $2$ of course)? The first $11$ :-) primes in this (infinite) series would be:  $3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041, \dotsc$  Many thanks!
Can I use the Twig template engine? I do a lot of  development and I like their templating language. , the , looks very much like it.  How can I use Twig in Drupal 7 or even Drupal 6? How to copy a file to multiple directories using the gnu cp command Google analytics: Tracking Not Installed How to convert light activated switch "Cannot find this file" error when deploying from Visual Studio 2010 I'm getting an error in Visual Studio 2010 after pressing F5 to Debug:     Error occurred in deployment step 'Add   Solution': Error: Cannot find this   file specified in the manifest file:   G2_SiteDefinition_List_Instances_Feature\ListInstance1\Elements.xml   But elements.xml file is there with the ListIntance1 folder. What am I missing here? The type initializer for 'Emgu.CV.CvInvoke' threw an exception If anyone who use Emgu openCv wrapper in .net 3.5 framework,please tell me why this exception appears,Its inner exception is unable to load cxcore.dll. I have never found experimental evidence that measuring one entangled particle causes the state of the other entangled particle to change, rather than just being revealed.  Using the spin up spin down example we know that one of the particles will be spin up and the other spin down, so when we measure one and find it is spin up we know the other is spin down. Is there any situation after creation that the particle with spin up will change to spin down? Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$ I am trying to prove that Given $\mathbb{R}$ as a vector space over $\mathbb{Q}$, and a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$.  Proof: Suppse that $|B|&lt;2^{\aleph_0}$, then $\mathbb R = span\{ b_i ; b_i \in B \}$ So $ \mathbb R = \{ \Sigma_{i=1}^{\infty}\alpha_i b_i ; \alpha_i \in \mathbb Q, b_i \in B, i \in \mathbb N \} = \bigcup_{n=1}^{\infty}\{\Sigma_{i=1}^n \alpha_ib_i\}$. Which is a contradiction since a countable union of countable union of countable sets is countable and $\mathbb R$ is not.  What do you think?  Thank you, Shir How can I blow out the background when shooting down for clothing on the ground? Why Java needs Serializable interface? Perfect set without rationals How do we know that entanglement allows measurement to instantly change the other particle's state? I have never found experimental evidence that measuring one entangled particle causes the state of the other entangled particle to change, rather than just being revealed.  Using the spin up spin down example we know that one of the particles will be spin up and the other spin down, so when we measure one and find it is spin up we know the other is spin down. Is there any situation after creation that the particle with spin up will change to spin down? How do you write this in LaTeX: I want to make some changes to Windows that require using the Group Policy Editor (gpedit.msc).  Unfortunately the Group Policy Editor is not included with the Starter Edition, Home and Home Premium editions of Windows.  How can I install it? In LWC am trying to iterate over a list and show the details from the list, this is working correctly , but as a header want to show the record number in a displayed order, below is desired outcome and simplified sample code.  Desired OutCome:   Employee Record 1: A  Employee Record 2: B  Employee Record 3: C   JavaScript:  Var empNames = ["A" , "B" , "C"];   HTML:  &lt;template for:each={empNames} for:item="employee" for:index="index"&gt; Employee Record{index} {employee} &lt;/template&gt;    Actual outcome  Employee Record 0: A  Employee Record 1: B  Employee Record 2: C   I understand as i am using {index} which indicated the position of element in an array which starts from 0 my actual outcome also starts like Employee Record 0 instead of Employee Record 1, but is there a simple way without writing much logic on JS to handle this in html and to make my headers starts from 1 instead of 0? Is there is any reason to make the permissions on an overridden C++ virtual function different from the base class?  Is there any danger in doing so?  For example:  class base {     public:         virtual int foo(double) = 0; }  class child : public base {     private:         virtual int foo(double); }   The  says that it is a bad idea, but doesn't say why.  I have seen this idiom in some code and I believe that the author was attempting to make the class final, based on an assumption that it is not possible to override a private member function.  However,  shows an example of overriding private functions.  Of course  recommends against doing so.  My concrete questions:   Is there any technical problem with using a different permission for virtual methods in derived classes vs base class? Is there any legitimate reason to do so? Can't do comparison on PageReference Windows 8 turns program sound volume down randomly I recently upgraded to Windows 8 from Win 7 64 bit and have started to encounter a strange issue. When I have any program running which plays sound, such as a game or spotify, after a random interval (usually around 5-10 minutes) the program sound will set itself really low.    If I Alt-Tab to the desktop and check the Mixer I can see that the Application volume has automatically set itself really low - the other volume levels (i.e. the Device speakers) stay the same.  I'm able to just set the application volume back to a reasonable level and it stays that way for another 5 - 10 minutes then goes quiet again.  My sound is Realtek High Definition Audio and my machine is an Acer Aspire 5738G if that helps in any way.  Any help much appreciated! How should I approach obvious proofs like these    I have been trying but couldn't find an elegant way to work these. Any help is highly appreciated ! Especially looking for a nice proof/hint for first problem Table of Contents for set of PDF files How to make Table of Contents for a set of PDF files?  Here's my code!  \documentclass{book} \usepackage{pdfpages} \usepackage[pdfauthor={&lt;somename&gt;},pdftitle={&lt;sometitle&gt;},pdftex]{hyperref} \usepackage{fancyhdr} \usepackage{tocloft} \usepackage[margin=0.5in,bottom=0.75in,top=0.75in]{geometry}   \pagestyle{fancy} \renewcommand{\headrulewidth}{0.4pt} \fancyhead[L]{X Y Z} \fancyhead[R]{} \begin{document}  \tableofcontents \newpage  \clearpage \phantomsection \includepdfset{pages=-,pagecommand=\thispagestyle{fancy}} \addcontentsline{toc}{chapter}{SAMPLE PDF 1\\ \textit{description}} \includepdf[pages=-]{template1.pdf}  \clearpage \phantomsection \addcontentsline{toc}{chapter}{SAMPLE PDF 2\\ \textit{description}} \includepdf[pages=-]{template2.pdf}  \clearpage \phantomsection \addcontentsline{toc}{chapter}{SAMPLE PDF 3\\ \textit{description}} \includepdf[pages=-]{template3.pdf}  \clearpage \phantomsection \addcontentsline{toc}{chapter}{SAMPLE PDF 4\\ \textit{description}} \includepdf[pages=-]{template4.pdf}  \clearpage \phantomsection \addcontentsline{toc}{chapter}{SAMPLE PDF 5\\ \textit{description}} \includepdf[pages=-]{template5.pdf}  \end{document}   Here's the output.    My problem is that the page number is not aligned with the title, it is aligned with the description. Also I'd like to put dots.   My desired output looks like this: