I have the following conjecture:     Let $k\in\mathbb{N}$ be even. Now $k+p$ is prime for infinitely many primes $p$.    I couldn't find anything on this topic, but I'm sure this has been thought of before. I tried to solve this using  and the , but no luck with those. Is this question equivalent to an existing open problem? If not, how can I prove this (I prefer hints, but I appreciate full answers, too)?  - Edit -  As has been pointed out in the comments, this is not a duplicate. I'm asking for infinitely many primes $p$ such that $p+k$ is prime, not only one.
Can every even integer be expressed as the difference of two primes? If so, is there any elementary proof?
What is the tolerable magnetic field (in Tesla) for a hard disk? I was wondering what would be the safest magnetic field for a hard drive so that the data inside it is safe and not wiped off?  For example I have a 2.1 home theatre system and when I take my android phone near it to check the magnetic field range it gives me a reading of 1000 micro Tesla. Would that be considered safe for a nearby hard disk? Approximating commuting matrices by commuting diagonalizable matrices Suppose the matrices $A$ and $B$ commute. Do there exists sequences $A_n$ and $B_n$ of matrices such that   $A_n \rightarrow A$, $B_n \rightarrow B$.  Each $A_n$ is diagonalizable  and the same for each $B_n$.  For every $n$, $A_n$ commutes with $B_n$.    Moreover, it would be nice if the following property was additionally satisfied: if $A,B$ are real, then $A_n,B_n$ can be chosen to be real as well. Books on Number Theory for anyone who loves Mathematics?(Beginner to Advanced &amp; just for someone who has a basic grasp of math) Why are C character literals ints instead of chars? In C++, sizeof('a') == sizeof(char) == 1. This makes intuitive sense, since 'a' is a character literal, and sizeof(char) == 1 as defined by the standard.  In C however, sizeof('a') == sizeof(int). That is, it appears that C character literals are actually integers. Does anyone know why? I can find plenty of mentions of this C quirk but no explanation for why it exists. How to move my cube left or right using touch Inputs (C#) in unity I am trying to create a 3d game in unity. I have a cube in unity and I want it to move left or right on swipe . It should move to a distance till where user swipe or take their finger off of a screen. I want it to move fast or the cube should move fast on swipe and cube should flow smooth. Like in the gif there is a circle and the user use their finger to move the circle till wherever the user swipe it and it should be instant and I want my cube to move like that at a distance till where user swipe their finger and it should be instant and fast.  I don't know how to do it. Any help is appreciated! About the absence of metal in machinery and buildings of the past I have recently created a logo. I have seen an online trend of showing off a logo in a realistic environment, illustrating possible use cases of the logo.  An example of this can be seen here, with the original logo at the bottom and a 3D mockup at the top:    How can I create such a mockup? ubuntu terminal is not working properly in vi editor What color can lightsabers be? I just saw the fan film  and the Force-sensitive bounty-hunter, Korbain Thor, wielded an ochre lightsaber (or at least that's what  described it as).   I'm just wondering if ochre is a canon color for a lightsaber? limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$ Show that $$\sup_{x\in [a,b]} f(x) = \lim_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$$ for f continuous and positive on [a,b].  I can show that LHS is greater than or equal to RHS but I can't show the other direction. Is there any way to tell Google to use a particular account for all Google services by default? I typically use 2 Google accounts simultaneously in my browser. So whenever I fire up any Google service like Google Maps or YouTube or Google Search, it uses one of the accounts. The problem is that I don't want that account to be used and no matter how many times I switch the account for these services, they seem to default to same account.  Is there any way to tell Google to use a particular account for all Google services by default?    I am not talking about using Google account to sign in to third party websites. I am talking only about Google's own services.  I am using Chrome if anyone is going to suggest client-side solution. Accuracy Vs. Precision  What I would like to know is whether I should use System.currentTimeMillis() or System.nanoTime() when updating my object's positions in my game?  Their change in movement is directly proportional to the elapsed time since the last call and I want to be as precise as possible.  I've read that there are some serious time-resolution issues between different operating systems (namely that Mac / Linux have an almost 1 ms resolution while Windows has a  50ms resolution??).  I'm primarly running my apps on windows and 50ms resolution seems pretty inaccurate.  Are there better options than the two I listed?  Any suggestions / comments? Refer to renamed columns in WHERE clause SELECT name, gdp/population as capita  FROM world w1  WHERE continent = 'Europe'       AND capita &gt;  (     SELECT gdp/population      FROM world      WHERE name = 'United Kingdom' );   How come I can't refer to capita in the WHERE clause? It returns this error:  Unknown column 'capita' in 'where clause'   I can however, run the query if I replace capita with gdp/population.  I don't want to do gdp/population &gt; .... How can I do capita &gt; ...? Or is this not possible? Sum of a Hyper-geometric series. (NBHM 2011) How to find the sum of the following series $$\frac{1}{5} - \frac{1\cdot 4}{5\cdot 10} + \frac{1\cdot 4\cdot 7}{5\cdot 10\cdot 15} - \dots\,.?$$  I have no idea. I have written the general term and tested its convergence by Gauss' test for convergence, but they are neither the question nor the answer. how to remove frost free outdoor faucet drain valve assembly I've tried unscrewing the part outlined in red below. No dice. Do I just need to remove the whole rod (above the red outline) and replace it?) If so, can anyone point me to instructions for them.  I can't see in there. Worried that I'll pull it out and not be able to put it back in.  (The deeper I go in the plumbing the more things I find that there is no modern fitting-part :)  My new assembly  replaces the parts outlined in red. the new assembly has a female thread. I am HOPING that the thicker part of the pipe (just above the black "collar" stopper)  is screwed onto the pipe above.  However, I cannot unscrew it. There is nothing to get a hold of. It's perfectly round. I've tried dw40, and let it sit for 20 minutes. No love.  I'll try wacking it with a board in the direction along which it moves in when it screws (perpendicular to the threads per [this answer][2]) Understanding imaginary exponents I've updated my Ubuntu to 19.10 couple of weeks ago and on installation system suggests to change or add shortcut for input source selection despite one was already defined previously. I've added ctrl+shift shortcut and just realized that it somehow overlapped any other ctrl+shift+something shortcuts globally, i.e. when I want to open new window in vscode, it opens new tab and it looks like system doesn't see the shift button press.   I tried to search this combination in shortcuts settings, but it's just not there. What is the safest way to move the iTunes Library from one hard drive to another? This may happen later with my iMac, but right now it is happening for my iTunes on PC.  The PC had 60GB of partition to install Windows 7, and right now it is down to about 2GB of free space.  All iTunes purchases, including Music and Movies, are downloaded to  C:\Users\mike\Music\iTunes\iTunes Media\Music  C:\Users\mike\Music\iTunes\iTunes Media\Movies   which will make the C: drive have less and less free space.  (and C: will be more healthy if it has at least a couple of GB of free space).  What is the safest, most proper way to migrate all the media to an external hard drive J: ?  On J:, the path might be:  J:\iTunes\iTunes Media\Music   or  J:\iTunes Media\Music   My guess is that we can change the folder in iTunes, but won't iTunes go to that folder or create it, and find nothing, and index everything wrong?  So, should an exact copy of C:\Users\mike\Music\iTunes\iTunes Media be made as J:\iTunes Media first (probably 30GB of files copying), and then start iTunes and change the preference for the folder to the J: one?  Is there a standard or official method to do this? Hanging indent inside list I would like items in a list to have a hanging indent (that is, for all lines after the first to be indented by a space or more),  but the traditional \hangindent command doesn't work for this.  \documentclass{article}  \begin{document} \hangindent=1cm This line of text has a hanging indent that looks fine, as long as it is outside a list environment. \begin{enumerate} \item \hangindent=1cm This line is inside a list environment and doesn't have a hanging indent- how can I add one? \end{enumerate} \end{document}     How can I add a hanging indent within a list? I'd never heard of anycast until a few seconds ago when I read "".  The wikipedia "" article on it is quite formal and doesn't really evoke a mental picture of how it would be used.  Can someone explain in a few informal sentences what "anycast" is, how you configure it (just in a general sense), and what its benefits are (what does it make easier)?