$$2 = 5-3 \\ 4 = 7-3 \\ 6 = 11-5 \\ 8 = 19-11 \\ 10 = 13-3 \\ \vdots$$  For every positive even number $n$, does there always exist a pair of prime $(p,q)$ such that $p-q =n$?
Can every even integer be expressed as the difference of two primes? If so, is there any elementary proof?
When I launch certain programs from the command line like eclipse and document viewer in 11.10 it spews a load of information that seems inconsequential.   Also when they are run in the background they sometimes continue to produce output to the terminal which I am currently working on, which is irritating.  I would like them just launch and keep the background stuff in the background. My reasoning is that if you launch these programs through the GUI (eg double clicking on an icon) these messages are never shown to me, so I don't need them in the command line. How does the summoning ability affect the encounter difficulty? The Drow Mage (CR 7) has the Action Summon Demon (1/day), which allows him to summon a shadow demon (CR 4). Is the shadow demon already included in the CR of the Drow Mage, or do I have to count the shadow demon as an extra creature to determine the difficulty of the encounter? In , the votes clearly show that the os.path.splitext function is preferred over the simple .split('.')[-1] string manipulation. Does anyone have a moment to explain exactly why that is? Is it faster, or more accurate, or what? I'm willing to accept that there's something better about it, but I can't immediately see what it might be. Might importing a whole module to do this be overkill, at least in simple cases?  EDIT: The OS specificity is a big win that's not immediately obvious; but even I should've seen the "what if there isn't a dot" case! And thanks to everybody for the general comments on library usage. Modifying .sty files? Yesterday I did some changes in the layout of my TeX document. I couldn't accomplish the changes until I opened the .sty files and modified some of their code. I am sure this is not the best idea. For one reason, after the packages got an update, I will have to modify the file again (and again and again).  Another way would be to create my own version of that .sty file and call that instead of the original one, but this might not be the best idea either. (again: at least the updates speak against it)  How can I accomplish the following changes by adding code to a local file (e.g. my .tex preamble) instead of changing global files (like the package .sty files)?  I wanted to change the following lines in ledmac.sty:  \def\printlines#1|#2|#3|#4|#5|#6|#7|{\begingroup   \setprintlines{#1}{#2}{#3}{#4}{#5}{#6}%   \ifl@d@pnum #1\fullstop\fi   \ifledplinenum \linenumrep{#2}\else \symplinenum\fi     %% #2 into: \arabtxt{\n{#2}}   \ifl@d@ssub \fullstop \sublinenumrep{#3}\fi   \ifl@d@dash \endashchar\fi   \ifl@d@pnum #4\fullstop\fi   \ifl@d@elin \linenumrep{#5}\fi   \ifl@d@esl \ifl@d@elin \fullstop\fi \sublinenumrep{#6}\fi \endgroup}   The second thing is a line in ledpar.sty:  \newcommand*{\l@dlinenumR}{%   \numlabfont\linenumrepR{\line@numR}\Rlineflag%       %% numlabfont into: numlabfontR   \ifsublines@     \ifnum\subline@num&gt;\z@       \unskip\fullstop\sublinenumrepR{\subline@numR}%     \fi   \fi}   (In the latter case, just adding \renewcommand with the modified code did not work.) remove files when name does NOT contain some words More options when flagging for migration I think there should be more Stack Exchange networks available when flagging a question to be migrated. For example I'd think that the following question:    ...would be a better fit on unix.stackexchange.com instead of Stack Overflow. But without the option to mark it so, I feel hesitant to mark it. Retrieve Preview Image URL of Salesforce Image Files How to setup two completely separate partitions on one SSD I have a MacBook with 1TB SSD. I want to have two separate partitions with two independent macOS installations. I want to make sure that none of the partitions have any kind of possibility to interact with the other, I want them to be as separated as if they were physically separate. Is this achievable with, for example, FileVault for each of them? Edit: My question is neither &quot;how can I install two different macOS versions on two different partitions on one SDD&quot;, neither &quot;how do I use FileVault&quot;, etc. I know how to do all of that. I want to make sure that there is no interaction between the partitions possible. Can this be made sure with the above approach? Is it sufficient? Does anyone know if there are any video formats (besides the HUGE uncompressed avis) that you can render in that maintain the alpha channel? (i.e. for after FX etc.)   I used to use quicktime, but that's no longer an option.  I know you can render in png. or other image formats, but video is significantly smaller, and I often work on machines with less space &amp; resources. Getting HTTP/2 Working on Apache 2.4.29 on Debian 8 I am trying to update my apache2 (Apache/2.4.29 (Debian 8)) server to support http2 but after enabling http2   with following code, it does not work because of mpm_prefork does not support http2  &lt;IfModule http2_module&gt;     ProtocolsHonorOrder On     Protocols h2 h2c http/1.1 &lt;/IfModule&gt;    since mpm_prefork apache (2.4.29)  does not work with http2, I tried using  mpm_event/mpm_worker but it does not work, so I enable mpm_prefork  sudo a2dismod mpm_event  sudo a2dismod mpm_worker  sudo a2enmod mpm_prefork   Since I am still running php5 what should I do to have http2 support on Debian8?  Will I have to update php5 to php7?  Is there any workaround to use mpm_worker/mpm_event with php5 with http2 support?  apache error log  [http2:warn] [pid 11992] AH10034: The mpm module (prefork.c) is not supported by mod_http2. The mpm determines how things are processed in your server. HTTP/2 has more demands in this regard and the currently selected mpm will just not do. This is an advisory warning. Your server will continue to work, but the HTTP/2 protocol will be inactive. [mpm_prefork:notice] [pid 11992] AH00163: Apache/2.4.29 (Debian) OpenSSL/1.1.0g configured -- resuming normal operations [core:notice] [pid 11992] AH00094: Command line: '/usr/sbin/apache2' Obtain screen status using ADB "This box of matches is empty" There are several Japanese books teaching Japanese students how to write in English. I found this example in  (Correcting Errors in English Composition Manuals) by Michio Kawakami and J.D. Monkman.  The authors of this book claim that this sentence is incorrect:     This box of matches is empty.   They note that a “box of matches” is a box containing matches (and not a box made for keeping matches), hence the sentence should instead be:     This matchbox is empty.   Likewise, an “empty bottle of beer” should instead be an “empty beer bottle.”  Is this actually an error that I should avoid in writing English? If so, is it a grammatical error or something else? What is the probability that $x_1+x_2+...+x_n \le n$? I am wondering if we should use  or  for buttons and headings in websites and web/mobile apps? Title Case: Manage my Account Delete my Account  Sentence case: Manage my account Delete my account  In  I found the recommendation 'choose your style and be consistent'. This is it? Aren't there any other (additional) recommendations or sources. Like for specific use cases or apps where the one style would be preferred over the other? Edit: The question refers primarily to English, but differences in other languages are also good to know. When looking at used camera bodies, a question that comes up a lot, is "how many shutter actuations, or clicks, does it have?"   What I am wondering is, how many is too many. In other words, is there a reference for knowing when a sensor is more likely to go? How should I judge a camera body with 20000 vs 5000? Is that a significant difference, or is that not even relevant.  Obviously this might something that is dependent on model, so if there is some information based on model that would be even more interesting.  One of the guys at Canon Tech Support said that this is completely irrelevant for the Rebel series cameras, but he is obviously slightly biased. :) How can I manage the "Open with Explorer" button based on user permissions? I am working on a problem and I am confused if exponents can be split up in the manner below.   $$x^{k+2} = x^{k+1}+x^{k+1} = 2x^{k+1} $$  I apologize if this is a simple question I tried to look up exponent rules but I couldn't find exponents + a number. Calculating centroids of polygon using ArcPy? I am trying to calculate the centroids of a polygon and add the x- and y-coordinate to their respective fields:  arcpy.env.workspace = r"C:/..."  input_fc = "shapefiles/precincts_v.shp" arcpy.AddField_management(input_fc, "X", "DOUBLE") arcpy.AddField_management(input_fc, "Y", "DOUBLE")  arcpy.CalculateField_management(input_fc, "X", "!SHAPE.CENTROID@DECIMALDEGREES!.split()[0]", "PYTHON")  arcpy.CalculateField_management(input_fc, "Y", "!SHAPE.CENTROID@DECIMALDEGREES!.split()[1]", "PYTHON")    but I an invalid syntax error. Where is the mistake?  Edit: exact error message  Traceback (most recent call last):   File "C:\Users\mquentel\Dropbox\PLSS\CA voting data\Python\CONSTRUCT_merge_voting_and_census.py", line 17, in &lt;module&gt;     arcpy.CalculateField_management(input_fc, "X", "!SHAPE.CENTROID@DECIMALDEGREES!.split()[0]", "PYTHON")   File "C:\Program Files (x86)\ArcGIS\Desktop10.4\ArcPy\arcpy\management.py", line 3360, in CalculateField     raise e ExecuteError: ERROR 000539: SyntaxError: invalid syntax (&lt;expression&gt;, line 1) Failed to execute (CalculateField). For a 2x2 matrix A satisfying $A^k=I$, compute $e^A$  Oh, the exponential of a matrix is: $e^A=\sum_{i=0}^\infty\frac{1}{i!}A^i$    I thought I'd solved the $e^A$ form but I actually did something really silly, now I'm a little stuck.  If $A^k=I$ then $A^{k+1}=A$ and we have a cycle forming, so we will get:  $$\sum^{k-1}_{i=0}\sum^{\infty}_{j=1}\frac{1}{(kj+i)!}A^i$$  (Or something like this form, I don't have paper to hand and just spotted that now)  Is this what the question wants? It doesn't use the 2x2 property.  I believe the answer lies in finding an expression for the inner summation, I can do this for two terms (think of $e+e^{-1}$ all the odd power leave) How do I install wine?