Suppose $N=111\dots1$ ($n$ ones). For which numbers $n$ is $N$ prime?  $n \ne 1, 3k$ is all progress I have made!
For which $n$ is the sum: $$\sum_{k=0}^{n}10^k$$ a prime number? Are they finite?
Use a .jar java library API in C#? I'm an entry level programmer so please be descriptive in your responses.  I am trying to use a Java API given as a .jar file in my C# .net application.  I don't know much Java, but this .jar file says "no main-class manifest attribute" when I try to run it so this means its a library?  This Java API also comes with a .java file which shows how to use the library but I cannot see the code inside the .jar.  I found  on this site, and one of the answers reads, "In simple way you can pack your java classes to jar file then In C# use Process class for execute and map IO stream."  I am semi-familiar with the Process class in C# but I don't understand how I could use it to use a Java library in my C# .net project.  Is this possible? or was that answer incorrect?  If so, could you explain how I can use the .jar library in my C# app. There is by now a captcha-problem When you first add a cylinder, you have the option to change the number of vertices, etc, but once you do anything else in blender, it seems you no longer can edit those parameters.   Is there a setting anywhere or an add-on that allows these parameters to be edited later on? If not, how easy would such an addon/feature be to create for anyone reading this? Relevant:  and   The answers in the linked question don't quite help me. Specifically, what happens with this case:  My three pens are green. Each of my three pens are green. Each of my three pens is green.  Part of the confusion seems to stem from the inclusion of &quot;three&quot;:  My pens are green. Each of my pens are green. Each pen is green.  There doesn't seem to be a way to rewrite the last example with &quot;three&quot;:  Each three pen is green.  The more common application would be:  All three pens are green.  But in the event that I want to say, &quot;Each of my three pens are green&quot; which is correct? And, in the event that the correct sentence is &quot;each of my three pens is green&quot; why does prepending &quot;each of&quot; to the beginning of &quot;my three pens are green&quot; change the verb? I'm entering the world of Linux and at work I'm using grep more and more.  By doing that I'm figuring out that sometimes it's not adequate for what I want.  I was struggling with grep a few days ago and a colleague of mine who is a senior Linux admin, told me to use awk. I was stunned by how fast I got a result.  So my question is when do you choose to use one over the other? What questions can I ask myself before going to work with grep and spending a lot of time, when I could have done it with awk and saved time? I cannot boot to the desktop because I filled the file system. How do I reclaim some space? My memory is completely full when I tried following the data recovery and copied the wrong file using command line tool Test Disk. As it was taking so long to copy, I turned it off and I realized I copied the wrong file. Now my laptop memory is now full and lead me to more problems.  I have had similar problems to :       Now my screen keeps blinking:   Can anybody help? Many thanks. Wish you all the best. I am trying to find a way with QGIS to get the intersection area of more than 2 layers.  All the tools in QGIS take just the 2 input layers.  For example in the image below, I have 4 layers and I want to retrieve just the black area.   Furthermore, I need to retrieve the count attribute and add it to the intersected area attribute table (in this case 4)    I know there is a tool that does the trick in ArcGIS, but is there a QGIS solution? I have a chromebook series 5. I want to install Ubuntu onto a USB stick. When I downloaded Ubuntu onto my USB stick, it won't start up.  Do I first have to download Ubuntu onto my chromebook hard drive, open Ubuntu and then make USB stick bootable? And then return back to chrome?  Or is there a way to download directly onto USB and make the stick bootable?  I appreciate any help. As we know, whenever school ends, Harry is sent back to live with the Dursleys, where he suffers from abuse. He would much prefer to live with the Weasleys, and often visits there before returning to school. It stands to reason that they probably don't live that far from each other, since:   Both Harry and the Weasleys use Platform 9&frac34; to get to school Ron was able to take Harry to the Burrow in a flying car within a reasonable amount of time   It's heavily hinted at that the Weasleys are poor. However, it's not like Harry would live there permanently. Three months isn't that bad, not to mention he's pretty well-off from his parents' money. There would be little to no extra expense on the Weasleys.  The only explanation is that Dumbledore goes out of his way to ensure Harry lives with the Dursleys. If so, why is this? Installing Wi-Fi driver for Realtek Semiconductor RTL8723DE Device [10ec:d723] unblock slime presta valve My Son's bike has slime inner tubes.  The bike has been sitting in the garage since last summer and the front tyres valve now seems blocked.  Its has what feels like 15-20 psi in it but I can not get the valve to let any air out or take any more in.  I have no idea at this point how to get it to unblock the valve so I can use it again.  For that matter I don't know how I could get the tire off as it has a reasonable (not ridable) amount of air in it without slashing the tyres (nice kings 2.2 which are pretty new).  I have tried putting the pump on it and putting a bit of air into it to try and clear the blockage but that didn't do anything.  Any ideas please? A probability theory question about independent coin tosses by two players Say Bob tosses his $n+1$ fair coins and Alice tosses her $n$ fair coins. Lets assume independent coin tosses. Now after all the $2n+1$ coin tosses one wants to know the probability that Bob has gotten more heads than Alice.    The way I thought of it is this : if Bob gets $0$ heads then there is no way he can get more heads than Alice. Otherwise the number of heads Bob can get which allows him to win is anything in the set $\{1,2,\dots,n+1\}$. And if Bob gets $x$ heads then the number of heads that Alice can get is anything in the set $\{0,1,2,..,x-1\}$. So\begin{align}P(\text{Bob gets more heads than Alice})&amp;= \sum_{x=1}^{n+1} \sum_{y=0}^{x-1} P( \text{Bob gets x heads }\cap \text{Alice gets y heads }) \\[0.2cm]&amp;= \sum_{x=1}^{n+1} \sum_{y=0}^{x-1} \left(C^{n+1}_x \frac{1}{2}^{x} \frac{1}{2}^{n+1-x}\right)\left( C^n_y \frac{1}{2}^y \frac {1}{2}^{n-y}\right)\\[0.2cm]&amp; = \sum_{x=1}^{n+1} \sum_{y=0}^{x-1} \frac{C^{n+1}_x C^n_y}{2^{2n+1}}\end{align}   How does one simplify this?      Apparently the answer is $\frac{1}{2}$ by an argument which looks like this, Since Bob tosses one more coin that Alice, it is impossible that they toss both the same number of heads and the same number of tails. So Bob tosses either more heads than Alice or more tails than Alice (but not both). Since the coins are fair, these events are equally likely by symmetry, so both events have probability 1/2. How do I go about porting Ubuntu Touch to different devices? What is the difference between test set and validation set? I found this confusing when I use the neural network toolbox in Matlab. It divided the raw data set into three parts:   training set validation set test set   I notice in many training or learning algorithm, the data is often divided into 2 parts, the training set and the test set.  My questions are:   what is the difference between validation set and test set?  Is the validation set really specific to neural network? Or it is optional. To go further, is there a difference between validation and testing in context of machine learning? We're in the process of deploying a private openstack instance but don't have the Swift object storage service available yet. Can juju bootstrap launch a utility instance without swift? I see that the openstack configuration control-bucket is a container id. register_nav_menus() won't register menus Please help with menu registeration:  I have followed this guide (http://codex.wordpress.org/Navigation_Menus) step by step.  Added the following code to functions.php:  function register_my_menus() {   register_nav_menus(     array('header-menu' =&gt; __( 'Header Menu' ) )   ); }  add_action( 'init', 'register_my_menus' );   But the guide says that this will make the menu appear in the Appearance -> Menus admin screen in the "Theme Locations" box as "Header Menu".  When I go to Appearance -> Menus everything is greyed out and there is no option of "Theme Locations" Let's say I want a way to display just the the center 50x50px of an image that's 250x250px in HTML. How can I do that. Also, is there a way to do this for css:url() references?  I'm aware of clip in CSS, but that seems to only work when used with absolute positioning. We already had multiple questions about unbalanced data when using , , ,  and a number of other similar questions, what makes it a very popular topic! Unfortunately, each of the questions seems to be algorithm-specific and I didn't find any general guidelines for dealing with unbalanced data.  Quoting , dealing with unbalanced data     (...) heavily depends on the learning method. Most general purpose   approaches have one (or several) ways to deal with this.   But when exactly should we worry about unbalanced data? Which algorithms are mostly affected by it and which are able to deal with it? Which algorithms would need us to balance the data? I am aware that discussing each of the algorithms would be impossible on Q&amp;A site like this, I am rather looking for a general guidelines on when it could be a problem. Lets say I have something like:   \[ Let x = number of cats \]   (This is a contrived example, but pretend we are actually inside a long align environment block...) "Let" and "number of cats" need to be written like normal text, while x= needs to be math type text.  I've seen this:  \[ \mbox{Let } x = \mbox{ number of cats} \]   and this:  \[ \textrm{Let } x = \textrm{ number of cats} \]   They seem to produce equivalent output, but I'm not sure which is the "correct" one. Also, they are not ideal in that the extra space needs to be placed inside the text mode block, otherwise it is ignored as math mode and butts the text right up against the math.  Ideally there would be some command which allowed embedding text into an equation, which correctly inserted leading and trailing space around the block as required without adding space inside the text block.  How does one do that "correctly"? Browse for Servers does not display local instance