I am trying to write a Python script that will find prime numbers. In the way that I am going about this, the script is going to take a number from a range, determine the factors, determine if the only two factors are 1 and itself, and return true if it's a prime number. I need help with my code to find the factors.   num = int(input("enter: "))  i = 1  while i &lt; num:   if num % i == 0:     print(i)     i += 1   else:     pass   The i is set to 1 because you can't divide by 0. However, the return starts to work, however, it only returns a couple of numbers, not the full list that I am hoping for. For example, you input 20, it returns only 1 and 2.
Here's the very dumb way:  def divisorGenerator(n):     for i in xrange(1,n/2+1):         if n%i == 0: yield i     yield n   The result I'd like to get is similar to this one, but I'd like a smarter algorithm (this one it's too much slow and dumb :-)  I can find prime factors and their multiplicity fast enough.  I've an generator that generates factor in this way:  (factor1, multiplicity1) (factor2, multiplicity2) (factor3, multiplicity3) and so on...  i.e. the output of   for i in factorGenerator(100):     print i   is:  (2, 2) (5, 2)   I don't know how much is this useful for what I want to do (I coded it for other problems), anyway I'd like a smarter way to make  for i in divisorGen(100):     print i   output this:  1 2 4 5 10 20 25 50 100     UPDATE: Many thanks to Greg Hewgill and his "smart way" :) Calculating all divisors of 100000000 took 0.01s with his way against the 39s that the dumb way took on my machine, very cool :D  UPDATE 2: Stop saying this is a duplicate of  post. Calculating the number of divisor of a given number doesn't need to calculate all the divisors. It's a different problem, if you think it's not then look for "Divisor function" on wikipedia. Read the questions and the answer before posting, if you do not understand what is the topic just don't add not useful and already given answers.
BGE everything white in playmode When I press P to play everything shows up white in the BGE. Shading is set to GLSL, and the objects are UV mapped and textured. It seems that vertex paint is overriding the material for the object even though it is unchecked in the material options.   Shading is set to GLSL   Objects have a texture applied What are the advantages and disadvantages of using ARC? What is the best way to get a sine wave from a square wave? could you help me on this integral ? $$\int \frac{1}{\cos(x)}\,\mathrm dx$$ Here's what I've started : $$\int \frac{1}{\cos(x)}\,\mathrm dx = \int \frac{\cos(x)}{\cos(x)^2}\,\mathrm dx = \int \frac{\cos(x)}{1-\sin(x)^2}\,\mathrm dx$$ Now, I did : $u = \sin(x)$, so $\mathrm du = 1$. Now I have : $$\int \frac{\text{???}}{1-u^2}\,\mathrm du$$ But at this point, I think I did the most of the job but I'm stuck. Could you help me to solve this integral please (to the integration by substitution at the end) ? Thanks EDIT : Now I follow the steps and I got : $$\int \frac{1}{1-u^2}\,\mathrm du$$ Doing the partial fraction I got $A = 1/2$ and $B = 1/2$. So basically I have : \begin{align} &amp; \int \frac{1}{1-u^2}\,\mathrm du = \int \frac{1/2}{1+u}\,\mathrm du + \int \frac{1/2}{1-u}\,\mathrm du \\[8pt] = {} &amp; \frac 1 2 \left(\int \frac{1}{1+u} \, du - \int \frac{1}{1-u} \, du\right) \\[8pt] = {} &amp; \frac 1 2 \ln\left(\frac{1+u}{1-u}\right) = \ln\left(\left(\frac{1+\sin(x)}{1-\sin(x)}\right)^{1/2}\right) \\[8pt] = {} &amp; \ln \left(\frac{\sqrt{1+\sin(x)}}{\sqrt{1-\sin(x)}}\right) = \ln\left(\frac{\sqrt{1+\sin(x)}}{\sqrt{\cos(x)^2}}\right) \\[8pt] = {} &amp; \ln\left(\frac{\sqrt{1+\sin(x)}}{\cos(x)}\right) \end{align} Here's what my teacher got :  What's wrong with what I did ? Did I miss something ? This is an attempt to write a canonical QA for this issue, as per the Meta post:   I expect it to be periodically edited with the goal of becoming a comprehensive information resource.  I have a MacBook Pro that has a key(Shift, Return,   Command, P, etc.) that doesn’t respond when pressed or is stuck in the down position.    It's possible that my favorite beverage was spilled (or some other liquid damage).  It's also possible that I have no idea what happened.  It was working yesterday and suddenly today it's no longer working.  Is there any way to bypass or remap the key?  Can I  have the system ignore it completely?  (This question can also apply to external USB keyboards or the Bluetooth keyboards) My script (should) acts differently, depending on the presence of the data in the input stream. So I can invoke it like this:  $ my-script.sh   or:  $ my-script.sh &lt;&lt;-MARK     Data comes...     ...data goes. MARK   or:  $ some-command | my-script.sh   where two last cases should read the data, while first case should notice the data is missing and act accordingly.  The crucial part (excerpt) of the script is:  #!/bin/bash local myData; read -d '' -t 0 myData;  [ -z "${myData}" ] &amp;&amp; {     # Notice the lack of the data. } || {     # Process the data. }   I use read to read input data, then option -d '' to read multiple lines, as this is expected, and the -t 0 to set timeout to zero. Why the timeout? According to  (typing left unchanged; bold is mine):     -t timeout time out and return failure if a complete line of input is               not read withint TIMEOUT seconds.  The value of the TMOUT               variable is the default timeout.  TIMEOUT may be a               fractional number.  If TIMEOUT is 0, read returns success only               if input is available on the specified file descriptor.  The               exit status is greater than 128 if the timeout is exceeded   So I in case 2 and 3 it should read the data immediately, as I understand it. Unfortunately it doesn't. As -t can take fractional values (according to above man page), changing read line to:  read -d '' -t 0.01 myData;   actually reads the data when data is present and skips it (after 10ms timeout) if it is not. But it should also work when TIMEOUT is set to real 0.  Why it actually doesn't? How can this be fixed? And is there, perhaps, alternative solution to the problem of "act differently depending on the presence of the data"?  UPDATE  Thanks to @Isaac I found a misleading discrepancy between quoted on-line version and my local one (normally I do not have locale set to en_US, so help read gave me translation which I couldn't paste here, and looking up for on-line translation was faster than setting new env---but that caused the whole problem).  So for 4.4.12 version of Bash it says:     If TIMEOUT is 0, read returns               immediately, without trying to read any data, returning               success only if input is available on the specified               file descriptor.   This gives a little bit different impression than "If TIMEOUT is 0, read returns success only if input is available on the specified file descriptor"---for me it implied actually an attempt to read the data.  So finally I tested this and it worked perfectly:  read -t 0 &amp;&amp; read -d '' myData;   The meaning: see if there's anything to read and if it succeed, just read it.  So as to base question, the correct answer was provided by Isaac. And as to alternative solution I prefer the above "read &amp;&amp; read" method. Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$ Find the maximum value of $f(x)$ when $0 \leq x \leq 1$ and $$ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$$   I'm guessing that the Fundamental Theorem of Calculus can't be used because the integrand is a function of $x$.  Any help would be greatly appreciated. There is a book I read in the 1980s or 1990s from a Ca.  library. It was a hard copy not a paperback. It is not "To Outlive Eternity/Tau Zero" by Poul Anderson (I have that one). It may have been written by a woman or someone whose last name starts with an "L".  A large crew of men and women are in a new super fast space ship. They are being chased by someone and they outrun the collapse of the universe, but they have lost their home planet. They watch as the universe is reborn. They go into orbit around a planet that looks like it can support life like theirs. They are moving super fast. They look like a ring of radiation going around the planet. They put down 10 super metal markers with scientific info onto the surface of the planet. They watch the planet develop and form life like the dinosaurs and then evolve into human like life forms.  There are 2 warring countries on the planet. They block or turn off the sun to freeze the planet and force the countries to form one world government. The planet gets freezing cold and the people start to freeze. The countries agree to form one world government. The people on the ship are welcomed to the planet. Prove that :  $$ \frac{\sqrt{\pi}}{2} e^{-\frac{a^2}{4} } =\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$$    the only thing I can think of is differentiating the RHS and trying to get :  $$ -2 f'(a) =a f(a) $$ But I couldn't do it.  Can anyone show me how to do this ? How do I select all but two types of entities in Minecraft with the type selector? I've asked this question towards a developer for Minecraft and I thought I'd ask here too since they might not see the question.  How do I select all but two types of entities in Minecraft?  For example, something like: /say @e[type=![Player,Item],r=50] (to clarify I also tried type=Item,Player, type=Item,type=Player etc)  Should select any entity that does not match players or items, so things like Creepers, Ghasts, XPOrbs, PrimedTNT and so on within a radius of 50 blocks and print them to the chat.  Instead it ignores one of the flags, and works with the other instead. How do I tell a Python script to use a particular version Is it worth cleaning the registry? I have heard that you should keep the registry clean on Windows. Is this actually important or is it just myth? How can a structure have infinite length and infinite surface area, but have finite volume? The limit of truncated sums of harmonic series, $\lim\limits_{k\to\infty}\sum_{n=k+1}^{2k}{\frac{1}{n}}$ How can I move my /home directory to another partition if it's already part of the / partition? I have a wonderful running Maverick Meerkat install going on right now. I want to move my /home to another partition as per many suggestions.   How can I go about doing this without reinstalling the entire Ubuntu system? Can I simply create the partition with gparted and then change the mount point of /home in fstab to reflect it or is it a bit more difficult? Coupon Collector Problem with Batched Selections I am trying to solve a variation on the .  In this scenario, someone is selecting coupons at random with replacement from n different possible coupons. However, the person is not selecting coupons one at a time, but instead, in batches.  Here's an example problem formulation: There are 100 distinct coupons. A person makes selections in 10-coupon batches at random (each coupon with replacement). What is the expected number of batches necessary to have selected 80 unique coupons?  I have been able to determine the expected number of selections necessary to have selected k unique coupons when selecting one at a time (much like Henry's ), but I'm a bit stumped as to how to go about solving it with this particular wrinkle.  Any tips/guidance would be greatly appreciated. Unknown error: '' ("The cache has no package named wine-staging-i386") Complex analysis : If $z =re^{i\theta}$, then prove that $|e^{iz}| =e^{-r\sin\theta}$ Problem :   If $z =re^{i\theta}$, then prove that $|e^{iz} | =e^{-r\sin\theta}$   My working :   $z = re^{i\theta} = r(\cos\theta + i\sin\theta)$   $\Rightarrow iz = ir(\cos\theta +\sin\theta) $ = $-r\sin\theta +ir\cos\theta $  $\Rightarrow e^{iz} =e^{(-r\sin\theta +ir\cos\theta)} = e^{-\sin\theta} e^{ir\cos\theta} $   $\Rightarrow |e^{iz}| = |e^{-r\sin\theta}||e^{ri\cos\theta}|$   Now please guide how to proceed further to get the result... thanks. When using divs when is it best to use a class vs id?   Is it best to use class, on say font variant or elements within the html? Then use id for the structure/containers?   This is something I've always been a little uncertain on, any help would  be great. What to do with meta questions referring to currently non-existing features? I sometimes come across such questions like that:    The "Not a real question" close reason doesn't exist for long time. It doesn't make sense to answer, comment, or even up/downvote (since there's nothing more to vote for/against it).   Shouldn't such questions be locked as historical ones? Should I flag them for moderator attention or just ignore them?