I know that $1$ is not a prime number, but what about $-1$?  Furthermore, what is the reason we categorise $1$ as not being prime?
From my understanding it's not prime because it's not greater than $0$. So my followup question is why did mathematicians exclude $-1$?  The definition of prime is having only two factors.   $-1 \cdot 1 = -1$
UK Standard Visitor visa application to sit for PLAB 1 without savings or job Can you help me with this inequality?  $|x-1| +|x+1| &lt;1$.  I think that it doesn't exist an $x$ that satisfies this inequality, but I'm not really convinced about my answer. Varnish cache with Nginx SSL termination How can I use varnish cache with nginx SSL termination for my SSL-Only (Https only) website? I use ubuntu 18.04 and I am currently running a wordpress site on my server. What resolution should a large format artwork for print be? For wall-sized graphics and large banners (e.g. 3m × 5m), what is an acceptable PPI for print? As I understand it 300 ppi is the typical for 'small' artworks (esp. for clean text resolution). However, for small artworks, the audience usually engages at a much closer distance. Therefore, in the interests of keeping a bitmap file down to a reasonable size, can you get away with a much-reduced PPI for a large format/banner print? Control a property with no socket (color ramp swatch, etc) from a Group Node input? How to hide password input from terminal in ruby script What exactly is the Box-Jenkins method for ARIMA processes? The  page says that Box-Jenkins is a method of fitting an ARIMA model to a time series. Now, if I want to fit an ARIMA model to a time series, I will open up SAS, call proc ARIMA, supply the parameters $p,d,q$ and SAS will give me AR and MA coefficients. Now, I can try different combinations of $p,d,q$ and SAS will give me a set of coefficients in each case. I select the set with the lowest Akaike information criterion.  My question is: where in the above procedure did I use Box-Jenkins? Am I supposed to use Box-Jenkins to come up with initial estimates of $p,d,q$? Or did SAS use it internally somehow? Justify text in moderncv cover letter I am writing a cover letter and CV using moderncv. Everything works fine so far, but the text in the cover letter is not justified. I think it is good that it is not hyphenated, but it would look much nicer if the text was justified.  Here is a minimal example:  \documentclass{moderncv} \moderncvstyle{classic}  \usepackage{lipsum} % just for dummy text  \firstname{John} \familyname{Doe}  \begin{document} \recipient{Prof.\ Dr.\ Foo Bar}{} \opening{Dear Professor Dr.\ Bar,} \closing{Yours sincerely,} \enclosure[Attached]{curriculum vit\ae}  \makelettertitle \lipsum[1] \makeletterclosing  \clearpage  \makecvtitle  \section{Education} \cventry{2009--present}{PhD Student}{here}{and}{there}{} \end{document} Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$ I've just installed Ubuntu 16.04 LTS on dual boot. I've looked for many solutions and tried them all but Chrome never starts; the logo appears on the left but no window opens.  I downloaded the deb file on google chrome website and installed it through Ubuntu Software, but it doesn't start.   I have tried installing it through the command line with   sudo dpkg -i --force-depends google-chrome-stable_current_amd64.deb sudo apt-get install -f   I have checked with uname -a and my system is 64 bit. I have also tried gdebi with the same result.   My repository universe is up to date.  I only have one display in settings>displays> so I can't turn off built-in display nor check the mirror display (I read it could be the problem as I also have a graphic card but it seems it is not in my case).  Here is what I get in the command line when I try to run Chrome from it ( the message is the same, whatever the method I used to install Chrome):  ~$ google-chrome [11831:11831:1122/114854.195473:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195493:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195508:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195515:ERROR:process_singleton_posix.cc(280)] Failed to create /home/basil/.config/google-chrome/SingletonLock: Permission denied (13) [11831:11831:1122/114854.195538:ERROR:process_singleton_posix.cc(433)] readlink failed: Permission denied (13) [11831:11831:1122/114854.195564:ERROR:process_singleton_posix.cc(256)] readlink(/home/basil/.config/google-chrome/SingletonLock) failed: Permission denied (13) [11831:11831:1122/114854.195622:ERROR:chrome_browser_main.cc(1498)] Failed to create a ProcessSingleton for your profile directory. This means that running multiple instances would start multiple browser processes rather than opening a new window in the existing process. Aborting now to avoid profile corruption. [11831:11868:1122/114854.209297:ERROR:browser_gpu_channel_host_factory.cc(108)] Failed to launch GPU process.   Any new approach will be much appreciated Can we apply for a Schengen tourist visa while visiting another country on a short-stay visa? Smart Phone's camera socket I just want ask how the socket in the image is called?   I couldn't really find and the closer I could get is only Raspberry's module. Rename All Files with a Certain Name I'm trying to find certain files with the name "stringx" and replace the name (but not the extension) with "stringy". So basically for stringx.txt and stingx.cs, I'd want stringy.txt and stringy.cs. I've attempted to test my rename command regex using following, but it returns no results:  rename -n 'stringx./s/\*$stringy./\/' stringx.*   I'm running csh under Centos. I can see that my regex is probably not correct, but I can't see any results to verify this. I can see that there are files that are named stringx. with the following:  find ./ -name 'stringx.*' I'm trying to make a map using the Javascript API.  I want to use my own basemap, but I can't find the most simple code to do this.  I always see something like this:    function init() {     map = new esri.Map("mapDiv", {       basemap: "satellite",       center: [-97.395, 37.537],       zoom: 11     });   But I don't want to use the ArcGIS online basemaps.  What is the code to make a map service I am hosting my basemap? C++ copy-construct construct-and-assign question prove that there are infinitely many numbers of the form $x = 111....1$ such that $31\mid x$ Is there any way to create a virtual file, such that reading from the file actually reads from the stdout of a command; writing to the file is acually writing to the stdin of a command?  So far I have kludged this with an inotifywait on a file, which calls a command when the file is modified, taking it's input from the file and writing back to it.  I don't like that the inotifywait has to be constantly restarted though (and I have to ensure that it is always running). I only use this file perhaps twice a week. Say I have some historical data e.g., past stock prices, airline ticket price fluctuations, past financial data of the company...  Now someone (or some formula) comes along and says "let's take/use the log of the distribution" and here's where I go WHY?  Questions:   WHY should one take the log of the distribution in the first place? WHAT does the log of the distribution 'give/simplify' that the original distribution couldn't/didn't? Is the log transformation 'lossless'? I.e., when transforming to log-space and analyzing the data, do the same conclusions hold for the original distribution? How come? And lastly WHEN to take the log of the distribution? Under what conditions does one decide to do this?   I've really wanted to understand log-based distributions (for example lognormal) but I never understood the when/why aspects - i.e., the log of the distribution is a normal distribution, so what? What does that even tell and me and why bother? Hence the question!  UPDATE: As per @whuber's comment I looked at the posts and for some reason I do understand the use of log transforms and their application in linear regression, since you can draw a relation between the independent variable and the log of the dependent variable. However, my question is generic in the sense of analyzing the distribution itself - there is no relation per se that I can conclude to help understand the reason of taking logs to analyze a distribution. I hope I'm making sense :-/  In regression analysis you do have constraints on the type/fit/distribution of the data and you can transform it and define a relation between the independent and (not transformed) dependent variable. But when/why would one do that for a distribution in isolation where constraints of type/fit/distribution are not necessarily applicable in a framework (like regression). I hope the clarification makes things more clear than confusing :)  This question deserves a clear answer as to "WHY and WHEN" I'm having a problem setting up a vhost on Apache 2.4, using CentOS 6.3.  This question seems to have been answered several times on this forum, but none of the solutions work for me.  Basically, I set up a vhost with a particular document root. When I attempt to access the site, I get a permissions error. But I have no problem if I use a different root.  More specifically, if I set the root to be /volume1/web/xxx, I get a 503 because of a permission problem on index.html.  But if I set it to be /volume1/web, the index.html comes up without a problem.  The details:   I set the persmissions on volume1, web, and xxx to 755. I set the permissions on the index.html files to 777. I copy the index.html file to both /volume1/web and /volume1/web/xxx, so that they have identical index files with identical permissions.   In httpd.conf, I set the VirtualHost options so that I can easily switch the document root by changing 2 comment marks  I have the following lines in the conf file:  NameVirtualHost *:80  &lt;VirtualHost *:80&gt;     ServerName localhost     #DocumentRoot /volume1/web     DocumentRoot /volume1/web/xxx      #&lt;Directory /volume1/web&gt;     &lt;Directory /volume1/web/xxx&gt;       Options Indexes FollowSymLinks Includes ExecCGI       AllowOverride All       Order Allow,Deny       Allow from all     &lt;/Directory&gt;      ErrorLog logs/localhost-error_log     CustomLog logs/localhost-access_log common &lt;/VirtualHost&gt;   These lines contain all the suggestions that worked for other people with the same problem.  What I get when I enter localhost in my browser depends on the document root.   If the root is /volume1/web, the index.html page comes up. if the root is /volume1/web/xxx, then I get a 503 error, and the apache error log has this line:  [Thu Jul 19 17:17:52 2012] [error] [client ::1] (13)Permission denied: access to /index.html denied   I also tried adding an index.php file to the directory. I then got permission denied messages for both the php file and the html file.  I also tried setting the user : group to apache : apache on the directories and files. That didn't help.  I've done everything I can think of to fix the permissions, to no avail.  Does anyone have an idea about what's happening here?  Thanks. What's a good back-up strategy for 1 desktop PC?