Is there any theorem connect to this problem?

It is a question I always ask when I was a primary student:

Could a number only contains digit’1′ with $ p$ digits writes $ $ A=\frac{10^{p}-1}{9} = \underbrace{11\cdots 1}_{p\text{ digits}}$ $ be a prime?

When $ p$ is not a prime, the factorization of $ A$ is obvious, but if $ p$ is a prime, the factorization of $ A$ may be subtle.

Here I made a list of some result for prime $ p$

$ $ \begin{array}{c|lcr} p & \ \text{factors} \ \hline 3 & 3 \times 37\ 5 & 41 \times 271 \ 7 & 239 \times 4649 \ 11 & 21649 \times 513239 \ 13 & 53 \times 79 \times 265371653 \ 17 & 2071723 \times 5363222357 \ 19 & \text{prime} \ 23 & \text{prime} \ 29 & 3191 \times 16763 \times 43037 \times 62003 \times 77843839397 \ 31 & 2791 \times 6943319 \times 57336415063790604359 \ 37 & 2028119 \times 247629013 \times 2212394296770203368013 \ 41 & 83 \times 1231 \times 538987 \times 201763709900322803748657942361 \ 43 & 173 \times 1527791 \times 1963506722254397 \times 2140992015395526641 \ 47 & 35121409 \times 316362908763458525001406154038726382279 \ 53 & 107 \times 1659431 \times 1325815267337711173 \times 47198858799491425660200071 \ 59 & 2559647034361 \times 4340876285657460212144534289928559826755746751 \ 61 & 733 \times 4637 \times 329401 \times 974293 \times 1360682471 \times 106007173861643 \times 7061709990156159479 \ 67 & 493121 \times 79863595778924342083 \times 28213380943176667001263153660999177245677 \ \end{array} $ $

I am not major in number theory, just curious again if there is any theorem or former work on this kind of question.

How to create a block “Search: More like this” with my articles?

I noticed that in the context filter of the view, there was a filter “Search: More like this”. How to make it work? Is this the right solution ?

I have a tags field on my articles with taxanomy terms. I would like to retrieve the taxonomy terms from this field in the current page and use them as keywords to search the body and title of all articles. To view similar articles.

How to create a block “Search: More like this” with my articles ?

Why am i getting this Drush error after updating a site?

I use Drush 8.1.17 to update my Drupal 7 sites, and as I have been updating my sites today after the latest security update I have noticed that after I update a site if I try to run any update related command (ex: drush up -n | grep available) I get this error:

The external command could not be executed due to an application error.                                      [error] The command could not be executed successfully (returned: PHP Fatal error:  Uncaught                         [error] TYPO3\PharStreamWrapper\Exception: Unexpected file extension in "phar:///usr/local/bin/drush/includes/.." in /srv/www/htdocs/fac-dev/misc/typo3/drupal-security/PharExtensionInterceptor.php:39 Stack trace: #0 /srv/www/htdocs/fac-dev/misc/typo3/phar-stream-wrapper/src/Behavior.php(72): Drupal\Core\Security\PharExtensionInterceptor->assert('phar:///usr/loc...', 'url_stat') #1 /srv/www/htdocs/fac-dev/misc/typo3/phar-stream-wrapper/src/Manager.php(83): TYPO3\PharStreamWrapper\Behavior->assert('phar:///usr/loc...', 'url_stat') #2 /srv/www/htdocs/fac-dev/misc/typo3/phar-stream-wrapper/src/PharStreamWrapper.php(412): TYPO3\PharStreamWrapper\Manager->assert('phar:///usr/loc...', 'url_stat') #3 /srv/www/htdocs/fac-dev/misc/typo3/phar-stream-wrapper/src/PharStreamWrapper.php(401): TYPO3\PharStreamWrapper\PharStreamWrapper->assert('phar:///usr/loc...', 'url_stat') #4 [internal function]: TYPO3\PharStreamWrapper\PharStreamWrapper->url_stat('phar:///usr/loc...', 2) #5 phar:///usr/local/bin/drush/includes/filesyste in /srv/www/htdocs/fac-dev/misc/typo3/drupal-security/PharExtensionInterceptor.php on line 39 , code: 255) pm-updatestatus failed. 

Does anyone know why this error only appeared after I updated the site and how I can fix it?

I’m not sure how to answer this and I don’t even know what type of math it is

I’m studying for a finals about probability distribution with Z-table and I got to this part in the example of my lecturer and I have no idea how she arrived to this answer, I’ve been staring at it and scratching my head for a good 30 minutes and still don’t know how she got it.

-2.33 = h-172/8 h = 153.4 

How did she get 153.4?

What is this style called?

I am trying to find the name of the style of the following websites. It’s a mix of classic bootstrap and material design. But instead of full material design it offers more depth and just looks a lot nicer.

  • -> the dropdown cards and feeling of depth on this one are amazing

I’ve seen more of this style lately and would like to know more about it. I really like the simple card style, especially the dropdown menu card on this site. There always seems to be some overlay of one element into another.

How to make this cypher more flexible and efficient

so I have been asked to make a cypher which can reverse the order of characters. Say “ajay” output “yaja”

so far i have used a very basic botched up code

 #include <iostream>  using namespace std;   int main() {     char a;     char b;     char c;     char d;      cout<< "enter word\n";     cin>>a;     cin>>b;     cin>>c; cin >>d;   cout<<d<<c<<b<<a;        return 0; } 

the code cannot work with lesser characters than 4 and obviously, it doesn’t work on characters greater than 4.

plus it just looks way too, crappy and direct. I have started coding from today itself so apologies in advance if the question doesn’t match the standards of the community.

How would you calculate this limit? $\lim\limits_{n \rightarrow\infty}\frac{\pi}{2n}\sum\limits_{k=1}^{n}\cos(\frac{\pi}{2n}k)$

I decided to calculate $ \int_{0}^{\pi/2}cos(x)dx$ using the sum definition of the integral. Obviously the answer is $ 1$ . I managed to calculate the resulting limit using the geometric series, taking the real part of the complex exponential function and several iterations of l’hopital’s rule. Are you able to simplify this absolute mess, i.e. find a better way of arriving at the desired answer?

$ $ \lim\limits_{n \rightarrow\infty}\frac{\pi}{2n}\sum\limits_{k=1}^{n}\cos(\frac{\pi}{2n}k)$ $

Every answer is highly appreciated =)

PS: If you want to see my solution, feel free to tell me! =)

Is this really prime number?

Using the primality test on this site ( I found that the concatenation of the digit reversal of the first 548 odd primes in the reverse order is a prime(!). It is a 1998-digit prime, but it took more than an hour for this ‘calculator’ to stated that it is a prime, it was a ‘super-slowly’ calculation. Could you confirm that this result is correct?. that prime is 7693749334931393…91713111753. Thanx.