C++ program elapse time
What do 'real', 'user' and 'sys' mean in the output of time(1)?
Where does a layman go to get a basic understanding of AKS primality testing. I am not talking about the optimal choice of $r$ (which I am told is the hardcore number-theoretic part of the algorithm). I mean basic things, like what does $\bmod(n, x^r-1)$ mean (how can something be mod two things?) And what does binomial expansion have to do with anything?  I can't find anything in Wikipedia that is appropriate for my level. Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$ What is given?  $$\text{Let P be a prime}$$ $$\text{Let} \space f(x)= 3x+1$$ $$\text{Let} \space g(x)= 6x+1$$  Show that: If there exists $x \in \mathbb{N}$ such that $f(x) = P $ , then there exists a $y \in \mathbb{N}$ , such that $g(y) = P$  What have I tried?   Given the question says 'show that', that leads me to believe I need to do a proof of sorts. I'm guessing it might be a proof by either strong induction, or just induction (or maybe just a direct proof?).  I don't even know how to set this up If $f(x) =$ $3x + 1 = $ prime...for any integer $x$, then there exists an integer $y$ such that $g(y) = 6y + 1 = $ prime?   Any hints or starting points would be greatly appreciated.   $$\text{Thanks in advance!}$$ Minecraft Forge 1.7.10 will not start My minecraft will not start on only that version, I have a Windows 7 computer with Java 8u20 installed, because the latest java 7 update will not work at all(plus imma dev for other stuff).   [22:26:39] [main/INFO] [LaunchWrapper]: Loading tweak class name   cpw.mods.fml.common.launcher.FMLTweaker  [22:26:39] [main/INFO] [LaunchWrapper]: Using primary tweak class name   cpw.mods.fml.common.launcher.FMLTweaker  [22:26:39] [main/INFO] [LaunchWrapper]: Calling tweak class   cpw.mods.fml.common.launcher.FMLTweaker  [22:26:40] [main/INFO] [FML]: Forge Mod Loader version 7.10.25.1208 for Minecraft   1.7.10 loading  [22:26:40] [main/INFO] [FML]: Java is Java HotSpot(TM) 64-Bit Server VM, version   1.8.0_20, running on Windows 7:amd64:6.1, installed at C:\Program   Files\Java\jre1.8.0_20  [22:26:40] [main/INFO] [LaunchWrapper]: Loading tweak class name   cpw.mods.fml.common.launcher.FMLInjectionAndSortingTweaker  [22:26:40] [main/INFO] [LaunchWrapper]: Loading tweak class name   cpw.mods.fml.common.launcher.FMLDeobfTweaker  [22:26:40] [main/INFO] [LaunchWrapper]: Calling tweak class   cpw.mods.fml.common.launcher.FMLInjectionAndSortingTweaker  [22:26:40] [main/ERROR] [LaunchWrapper]: Unable to launch  java.util.ConcurrentModificationException     at java.util.ArrayList$Itr.checkForComodification(Unknown Source) ~[?:1.8.0_20]     at java.util.ArrayList$Itr.remove(Unknown Source) ~[?:1.8.0_20]     at net.minecraft.launchwrapper.Launch.launch(Launch.java:117) [launchwrapper-  1.9.jar:?]     at net.minecraft.launchwrapper.Launch.main(Launch.java:28) [launchwrapper-1.9.jar:?]  Java HotSpot(TM) 64-Bit Server VM warning: Using incremental CMS is deprecated and   will likely be removed in a future release Do reactions interrupt their triggers or not? In the Player's Handbook, it is pretty clear that reactions normally interrupt the thing that they are reacting to.    Xanathar's Guide to Everything, however, has explicitly changed all reactions to occurring after their triggers have finished resolving unless the ability specifies otherwise, and is reliant on that implicit assumption for several reaction abilities already.  This leads to contradictory interpretations of reactions that take implicit timing. How should this be resolved?   I'm particularly interested in how to resolve this in Adventurers League games, where players show up with perfectly legal characters reasonably expecting their abilities to work either way on account of owning or not owning XGE. How do I pack textures for sending off to a render farm Whenever i try to send a project off to a render farm such as sheepit, it says it needs the textures packing with the file in order to render correctly.  How would I do this? How can I calculate how long it will take to transfer a file over LAN? I want to know about the method with which we can calculate data transfer speed.   If I am sending a 1 GB file through a 1 Gb/s LAN connection, from one computer to another, how much time will it take to transfer that file? Is there a word to describe someone who tends to disagree with others only to upset them? How should duplicate questions be handled? What should I do when I see a question that is a duplicate of another one?   Should I answer it? Should I downvote it? Should I comment? Should I edit the question to indicate it's a duplicate? If I can, should I (vote to) close the question? What happens when I vote to close as duplicate? Or: Why did a comment with my name on it just appear? Should I flag it for moderator attention? What about similar or related questions? What is the source for defaulting to plain English readings of non-game terms? How to make a sound once a process is complete? I have started a long process through a terminal. Is it possible to make the Ubuntu terminal make a sound once the process is complete? This way, I don’t need to keep checking, but will instead be notified through a sound. Is it possible to paint only inside a stroke on illustrator? what i actually want to do is paint the same stroke with different colors in diferent segments of it but i can't do it...   Also... I've seen some tutorials that include editing a gradient but that would be very complicated and so would be to make a new stroke over this one, I just hope theres an easyer way XD  Edit per comment:  thats cool but not really what im looking for, what i want is lets say my stroke has the shape of a burger i want part of i to be bread color and part of it to be meat color... not one stroke over the other... i want something like this, imagine the jelly worm is my stroke: Holomorphic function has at most countably zeros Let $f$ be holomorphic in a domain $U$, then $f$ has at most countably zeros.  How can I prove this statement? I have seen it in Sheng Gong  explicitly, but without any indications. Let $(X,d)$ be a metric space and let $S$ be the set of Cauchy sequences in $S$. Define "~" in $S$ by "$\{s_k\}$ ~ $\{t_k\}$" to mean that $d(s_k,t_k) \to 0$ as $k \to \infty$. Let $X'$ denote the set of equivalence classes of $S$ and let $s'$ denote the equivalence class of $s = \{s_k\}$.   I know $\phi(s',t') = \lim\limits_{k \to \infty} d(s_k,t_k)$ is a metric on $X'$.   Show $(X',\phi)$ is complete.  For $x \in X$, define $x'$ to be the equivalence class of the constant sequence ${x,x,...}$. Show that the function $x \to x'$ is an isometry of $X$ onto a dense subset of $X$.   If anyone can share a proof, or steer me in the right direction, maybe tell me what it is that I need to prove specifically, that would be great. "Being" or "to be"? Which is better structured?     "She loves to be herself instead of showing off"    or     "She loves being herself instead of showing off"   or     "She loves being and not appearing" The functions of each pair are inverse to each other. For each pair, check that both compositions give the identity function.  $F: \mathbb{R} \to \mathbb{R}$ and $F^{−1}:\mathbb{R} \to \mathbb{R}$ are defined by $F(x)=3x+2$ and $F^{−1}(y)=\dfrac{y−2}{3}$. for all y ∈ R  My attempt:     Inverse Function  For each particular but arbitrarily chosen $y \in \mathbb{R}$, according to the definition of $f^{-1}$, $f^{-1}(y) = \dfrac{y-2}{3}$ is a unique real number $x$ such that $f(x) = y$. \begin{align*} F(x) &amp; = y\\ 3x + 2 &amp; = y\\ x &amp; = \frac{y-2}{3} \end{align*} Therefore, $f^{-1}(y) = \frac{y-2}{3}$.  Compositions of Functions  The functions $g \circ f$ and $f \circ g$ are defined as follows: $$(g \circ f)(x) = g(f(x)) = g(3x + 2) = 3x + 2$$  for all $x \in \mathbb{Z}$. How to limit charging to a user defined limit? My UleFone Armor 2 has a 4700mAh battery and I would like to limit the charging to 60% to reduce battery aging. The batteries in most of the phones are not user-replaceable and I am worried that a factory/service battery replacement might affect water resistance negatively.  How can I limit the charging to 60%? (But not limiting charging speed. I love fast charging.)  Lenovo ThinkPads have a built-in feature that does this, called “battery preservation mode”. I have a dual screen setup on my laptop (using 12.04 LTS) using a HDMI connected display. Everything works fine, but everytime I connect/disconnect the cable I have to go to Sound preferences and change the sound output device manually.  Is there any way to change the sound output device on connect/disconnection of cable, so when I connect my display the sound output is set to HDMI and when I disconnect it the sound goes back to laptop speakers? Best word for "unable to change" Showing there is no ring whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$ Show that there is no commutative ring with the identity whose additive group is isomorphic to $\mathbb{Q}/\mathbb{Z}$. RemoveDuplicates gives 1004 error