"It's well known that there are infinitely many prime numbers, but   they become rare, even by the time you get to the 100s," Ono explains.   "In fact, out of the first 100,000 numbers, only 9,592 are prime   numbers, or roughly 9.5 percent. And they rapidly become rarer from   there. The probability of picking a number at random and having it   be prime is zero. It almost never happens."      --Source:    I feel really skeptical about the statement in bold above. I think the probability tends to approach zero but can never be zero. Please explain how the probability is being calculated mathematically?
I read an essay about prime numbers. In it the author suggests that a natural first question to ask is,      What is the probability of a random natural number being prime?   but proceeds to dismiss it as "not making sense". I wonder what's wrong with the question. Is its meaninglessness related to the fact that there is an infinite number of naturals?
How can I prevent iPhoto/Photos/Image Capture from launching everytime I plug in my iPad/iPhone? How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? What partitioning scheme do you recommend for a desktop? I've always created three or four primary partitions -- root, swap, home, and sometimes a separate boot partition. Ubuntu's default install offers LVMs. I've never had to add additional drives or space, so it never seemed like a big deal. Whenever I do a fresh install, though, I always think there might be a better way. I'm working in C, and I have to concatenate a few things.  Right now I have this:  message = strcat("TEXT ", var);  message2 = strcat(strcat("TEXT ", foo), strcat(" TEXT ", bar));   Now if you have experience in C I'm sure you realize that this gives you a segmentation fault when you try to run it. So how do I work around that? every planar graph can be expressed as a union of five edge-disjoint forests How can I prove that every planar graph can be expressed as a union of (maximum) five edge-disjoint forests?  Only thing I can think about is going somehow like the $5$ color theorem but I get stuck in the middle. Or with induction, but still something doesn't fit. Can you help? Automatically show which tags were edited in revision history I’ve developed the habit of using the revision summary to indicate which changes I’ve made to the tags while retagging a question.  For instance, if the question originally had tags   and it should be  instead, I write the following in the revision summary:     Edited tags: -cocoa, -touch, +cocoa-touch   which I find useful (and potentially educational) for the OP and other editors.  On the other hand, when an editor doesn’t type a revision summary, Stack Overflow shows     User (timestamp) edited tags   with no indication of the difference between previous tags and the tags set by that edit.  Since there’s a limit on the number of tags, this difference would easily fit in the revision history list of that question. Could this be automatic in case the editor doesn’t fill the revision summary? Is it worth it? PHP not working after upgraded to Ubuntu 17.10 After I upgraded to Ubuntu 17.10, PHP totally stopped working. Everything works fine in Ubuntu 17.04. The code for info.php as follows does not work:   &lt;?php  phpinfo(); ?&gt;   It is not showing PHP information, it only shows the source code like above. Why is "what can I ask about here" not the first entry in the help center? On a lot of sites, the first section of the Help Center looks like this:    When I go to a site's help center it's almost always to find out what's on-topic there, because I'm considering asking or migrating a question.  Leading with what not to ask seems odd to me, and I suspect that to someone not already familiar with SE it could be a little off-putting.  It's not always like this, though; here on MSE we get this, which I've seen on some other sites too:    That ordering makes a lot more sense to me.  It's also consistent with the tour.  (Maybe "how do I ask a good question?" should also be "above the fold", in the top five somewhere.)  Why the difference?  Can we either make the order consistent across the network and more logical, or give users or moderators the ability to change the order on their sites? I would like to put an address in my document as follows:  |                             | |                     Name    | |                     Street #| |                     City    | |                     ZIP     | |                             |   where the | mark the left and right page borders. I would like the items of the address (Name, Street etc.) to be left-flushed, but the box right-flushed so that the longest item touches the right page border.  Is there a simple way to accomplish this? Inclusion of Fields whose order is a prime power Blue was correct, I need to fix my understanding of this:     Finite fields have cardinality of a prime order because they have a prime subfield that has finite characteristic.    I do not completely understand why finite field of each characteristic is unique. Perhaps we look at a polynomial and express the finite field as a splitting field? And we use uniqueness of splitting fields?  Then, why is it that  $\mathbb F_{p^m} \subseteq \mathbb F_{p^n}$ if and only if $m$ divides $n$? Unable to understand the syntax of the command find The find command seems to differ from other Unix commands.  Why is there the empty curly brackets and a backward flash at the end of the following command?  find * -perm 777 -exec chmod 770 {} \;   I found one reason for the curly brackets but not for the backward flash.   The curly brackets are apparently for the path     Same as -exec, except that ``{}'' is   replaced with as many pathnames as   possible for each invocation of   utility I've seen some of the other threads on using strings as x axis labels, but nothing that fits my situation.  I'm trying to create a bar chart from a CSV file. I can do it so long as everything in the data is numeric. However, in my actual data table, the first row is multi-word string descriptions. I need these descriptions to be the x axis labels for each bar.  I've tried symbolic x coords, but I get the "could not parse input as a floating point number" error. I've also tried adding an ID column and using that as the x values, and assigning xtick labels as the string descriptors. I get the same issue that way.  Here's an attempt at an MWE:  \documentclass{article}  \usepackage{lmodern} \usepackage{tikz} \usepackage{pgfplots} \usepackage{pgfplotstable}  \begin{document}  \pgfplotstabletypeset[columns/category/.style={string type},col sep=comma]{Book3.csv} \vspace{1cm}  \begin{tikzpicture} \begin{axis}[ ybar, xlabel=Xstuff, ylabel=Value, symbolic x coords={cat a,cat b,cat c,cat d,cat e,cat f,cat g}, %xtick labels={cat a,cat b,cat c,cat d,cat e,cat f,cat g},% this is from when i tried the xtick label method xtick=data, nodes near coords, nodes near coords align={vertical}] \addplot table[x=category,y=value]{Book3.csv}; %\addplot table[x=category,y=value]{Book3.csv};&amp; again, from trying the xtick label method  \end{axis}  \end{tikzpicture} \end{document}   Since I suspect this might get answered quickly by you chart gurus, I have a follow-up question:  I have to do a bunch of these charts, and I would like to automate the symbolic x coords process. Is there a way to populate the dictionary of accepted x coords by reading a column of the data? (something like symbolic x coords={columns/category/{Book3.csv}} )?  Book3.csv looks like this (ignore the ID column if using the xtick label method):  ID, category, value, value 2 1,  cat a,    1,     7 2,  cat b,    2,     6 3,  cat c,    3,     5 4,  cat d,    4,     4 5,  cat e,    5,     3 6,  cat f,    6,     2 7,  cat g,    7,     1 E.g.: If your Gmail ID is abc.xyz@gmail.com, it considers this the same as abcxyz@gmail.com.  Why is this so? Beamer continue block in next column Rendering low and res/high res images Is it possible to render in Blender with reduced low res files and then ask Blender to render the final render with 4k high res files? Low and high res files would be numbered identically but would be located in different folders.  Many thanks What is the best way to unit test a method that calls into multiple methods, for example:  modify(string value) {     if(value.Length &gt; 5)  replaceit(value);      else changeit(value); }   This pseudo code has a modify method that (currently) calls either replaceit() or changeit(). I have already wrote tests for replaceit and changeit, so writing a new test for modify will be 99% the same set of code.  I need to test it thought because it may change in the future.    So do I copy paste the existing test code?  Move the test code to a common function?  Any other ideas?  I'm not sure of the best practice here. I am having the same trouble as others getting my Atheros AR8131 Ethernet card recognised by Ubuntu 12.10 on my new HP Pavillion P7-1449 PC. I found the same question where the answer suggested the following:   Download Tarball compact-wireless-3.6.8-1-snpc Run  ./scripts/driver-select alx make sudo make install    The problem is when I run the make command I get the following:  make -C /lib/modules/3.5.0-21-generic/build M=/home/chris/Downloads/compat-wireless-3.6.8-1-snpc modules make: *** /lib/modules/3.5.0-21-generic/build: No such file or directory.  Stop. make: *** [modules] Error 2   Found a link to an alternative patch file (compat-wireless-2012-09-25-pc) but then I get the similar error:  make -C /lib/modules/3.5.0-21-generic/build M=/home/chris/Desktop/compat-wireless-2012-09-25-pc modules make: *** /lib/modules/3.5.0-21-generic/build: No such file or directory.  Stop. make: *** [modules] Error 2   Any help you could provide would be greatly appreciated. SQL injection that gets around mysql_real_escape_string() How to configure Remote Desktop on my office Ubuntu machine and how to connect to it from my Windows laptop at home? How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$? Show that $$n! \leqslant \left(\frac{n+1}{2}\right)^n \quad \hbox{for all } n \in \mathbb{N}$$  I know that it can be done by induction but I always find line where I do not know what to do next.