Let $f(x) = x^2 + x + 41$. Show that $f(n)$ is prime for $0 \le n \le 39$, but $f(40)$ is composite.
Is the notorious $n^2 + n + 41$ prime generator the last of its type?
Why doesn't current pass through a resistance if there is another path without resistance? Why doesn't current pass through a resistance if there is another path without resistance? How does it know there is resistance on that path? Some clarification:  I understand that some current will flow through the resistance. A depiction of this phenomenon through Ohm's laws does not answer the 'why' part of the question as it does not illuminate the process behind this phenomenon. There seems to be disagreement among the answers on whether the charge repulsions are enough to cause this effect. Cited research would be appreciated to resolve this issue. To refine what I mean by this question, I think I should give an example of why I am curious as to the causal background of this phenomenon. If charge repulsions do in fact repel 'current' in the example of the short circuit, then why does the same phenomenon not happen in other parallel circuits. (Again, I know that not all circuits behave ideally) I believe the question is expressed in the most straightforward way possible. This should, however, not affect the scope of the answers. I do not wish to see or think on the level of an electron as circuit behavior always includes a cumulative effect due to the nature of electrostatic interactions. How is being able to break into any Linux machine through grub2 secure? What happened to Control.InvokeRequired in WPF? I am looking for a injective cochain map $\psi: C^*\rightarrow D^*$ such that the map $\Psi^i$ from $C^i$ to $D^i$ is injective, but the map $\psi^*$ from  $H^i(C^*)$ to $H^i(D^*)$ is not injective for any $i\geq0$. Black is Back! New update with Achievement shows black backgrounds with black text Update: This is fixed on version 1.0.43 as per the accepted answer below.  Already saw ,  and . They are old and seem to be about previous versions.  I just updated to the version 1.0.41 of the Android app that brings the new feature - Achievements. Sadly, I think the stress of World Cup has made you guys not do a good job with it. It's buggy.  When I open my Achievements panel and tap on any post, I get this:    After I get this, it persists throughout the rest of the app. For example, if I go to the feed and open another question, I get this too.  Detailed reproduction steps are available in AD7six's answer.  My Device: Samsung Galaxy SIII LTE GT-I9305 Android: Stock ROM 4.3 Jelly Bean  Other Devices: - Device model, Android version, Reported by - HTC Desire, 4.2.2, xd6_ - Huawei Ascend, 4.2, Manu343726 - LG Optimus F3, 4.1.2, Rocket Hazmat - LG Optimus G, 4.3, Canadian Luke - Samsung Galaxy Nexus (Sprint), 4.3, Chrono Kitsune - Samsung Galaxy Note II, 4.3, Katja Christiansen - Samsung Galaxy SII GT-I9100, 4.1.2, AD7six - Sharp SH837W, 4.1.2, timrau - Sony Xperia SP, 4.3, pepoluan - Sony Xperia Z1, 4.3, user2313067 - Unknown, 4.2.1, Deer Hunter Particularly, does proc always list the VmRSS value in kB? I can't find a solid answer on the , although it appears that it sticks to one unit. Formula for the $n$th term of $1, 2, 2, 3, 3, 3, 4, 4 ,4, 4, 5, ...$ There exists a formula for the $n$th term of this sequence  from the OEIS ("$n$ appears $n$ times") $$1, 2, 2, 3, 3, 3, 4, 4 ,4, 4, 5...$$ which is $$\left \lfloor \frac {1+\sqrt{1+8n}}{2} \right \rfloor.$$  Is there a better formula for the $n$th term? A formula that isn't a 'magic' one that just happens to work but one that comes from a well-founded observation. Preferably one not using the floor function. I also have suspicions about the sustainability of the above formula as I feel with very $n$ it may not function properly. Can we use an Android phone as a Wi-Fi repeater? Can we use an Android phone as a Wi-Fi repeater?  Imagine situation when you can access a weak Wi-Fi signal from a free hotspot (coffee shop) signal near window, but want to work in the middle of the room. Then we can put the phone on the window sill to spread the signal over the entire home.  Is it feasible? I am trying to use the Directory.GetFiles() method to retrieve a list of files of multiple types, such as mp3's and jpg's.  I have tried both of the following with no luck:  Directory.GetFiles("C:\\path", "*.mp3|*.jpg", SearchOption.AllDirectories); Directory.GetFiles("C:\\path", "*.mp3;*.jpg", SearchOption.AllDirectories);   Is there a way to do this in one call? Catenatives followed by infinitives and gerunds I'm using iPhone 6s 16 GB. My storage isn't full but still I can't download anything. Every time I wanted to start a download it keeps telling:  app name* could not be download at this time Schengen refusal formulae can be difficult to understand sometimes.  Sometimes an applicant receives a refusal with:       Justification for the purpose and conditions of the intended stay was not reliable.     often accompanied by:       Your intention to leave the territory of the Member States before the expiry of the visa applied for could not be ascertained.   What is meant by this refusal reason?  What are they trying to say? What do the fields in ls -al output mean? What is the most elegant way to check if the directory a file is going to be written to exists, and if not, create the directory using Python? Here is what I tried:  import os  file_path = "/my/directory/filename.txt" directory = os.path.dirname(file_path)  try:     os.stat(directory) except:     os.mkdir(directory)         f = file(filename)   Somehow, I missed os.path.exists (thanks kanja, Blair, and Douglas). This is what I have now:  def ensure_dir(file_path):     directory = os.path.dirname(file_path)     if not os.path.exists(directory):         os.makedirs(directory)   Is there a flag for "open", that makes this happen automatically? How Does One Transfer A Steam Game? I have a failure to transfer my game from one HDD to another, and one PC to another. I copied the entire Skyrim folder from one HDD to another. And told where to find it also. Steam did a huge check of my HDD.  But it ended up downloading most of the files anyway. It took a week to download Dawnguard, Hearthfire, and Dragonborn files along with my Hi-Res textures.  I did ask about it in chat. But I feel this could help me or somebody else.  This is the screen I am looking at after transferring my entire hard drive to to new one. Steam downloaded my games, including Skyrim even though my Skyrim data folder had all the data files for Dawnguard, Hearthfire, Hi-Res and Dragonborn.  I have my copied files and have got rid of everything not steam related. I just have my DLCs and they include my hires files.  This is what it looks like.    But I still get this :     What could be causing this? How can I rectify? And in future when one is migrating to a new PC, how can this be avoided?  EDIT::::::::::::::::: Removed everything : Here is how it looks :  Still the prompt as before Steam Error 15  (Side Note : I transferred all my Origin games just by copy/pasting. This really is not nice.)    EDIT 2 :::::::::::::::::::::  And one more EDIT  I tried getting game cache up to speed, but this is prompt I am getting. But I played the game, it was working, I could pick out my character and all, and escape from Helgen.  EDITED 3 :::::::::::::::::  How does one transfer a Steam game? A game that is heavily modded, will the backup a Steam Game option suffice? While studying the problem of determining the orbit of a binary star system, my astronomy notes say: "the projection of an ellipse onto a plane is still an ellipse (except the special case in which it's a segment)". How could I prove this?  EDIT: As suggested i'm adding what I know about ellipses. I know the basics of ellipses in the plane, the equation of an ellipse in a plane in cartesia coordinates, the equation of an ellipse in polar coordinates, the fact that ellipses can be obtained by the intersection of planes with a cone. In my geometry course we defined ellipses as the the points of the plane such that the ratio between the distance from a point and a line is constant and less than 1. I also know that the sum of the distances of the points of the ellipse from the foci is constant. If $11z^{10}+10iz^9+10iz-11 = 0$. Then possible value of $\mid z \mid,$ is If $11z^{10}+10iz^9+10iz-11 = 0$. Then possible value of $\mid z \mid,$ is  $\bf{My\; Try::}$ Given $11z^{10}+10iz^9+10iz-11 = 0\Rightarrow \displaystyle z^9 = \frac{11-10iz}{11z+10i}.$  Now Put $z = x+iy\;,$ we get $\displaystyle (x+iy)^9 = \frac{11-10i(x+iy)}{11(x+iy)+10i} = \frac{(11+10y)-10ix}{11x+i(10+11y)}$  Now i did not understand how can i solve it,  Help Required  Thanks How can I install Ubuntu encrypted with LUKS with dual-boot? The Ubuntu installation disk has an option to install Ubuntu encrypted using LUKS. However, there is no option to perform an encrypted installation along-side existing partitions for a dual-boot scenario.  How can I install Ubuntu encrypted alongside another partition from the live disk? Can I fail to deserialize with XmlSerializer in C# if an element is not found? I am using XmlSerializer to write and read an object to xml in C#.  I currently use the attributes XmlElement and XmlIgnore to manipulate the serialization of the object.  If my xml file is missing an xml element that I require, my object still deserializes (xml -> object) just fine.   How do I indicate (preferably via Attributes) that a certain field is "required"?  Here is a sample method of what I am using currently:  [XmlElement(ElementName="numberOfWidgets")] public int NumberThatIsRequired {     set ...;     get ...; }   My ideal solution would be to add something like an XmlRequired attribute.     Also, is there a good reference for what Attributes are available to manipulate the behavior of XmlSerializer? What Easter eggs do the chat sites have? According to , the SE chat sites may have individual Easter eggs, depending on the site. If you find them, please post. Because it's so easy to make this stuff up, a screenshot as proof would be nice. (Although Photoshop isn't that hard either...)