For every positive even number $n$, does there always exist a pair of prime $(p,q)$ such that $p-q =n$?
Can every even integer be expressed as the difference of two primes?
Have a seat, guys   I think "have a seat" is a fixed phrase that does not change whether you address someone or a group of people.  Is that correct?  If you have more to add to the post, please do so as I would love to know more. How to enable numlock at boot time for login screen? I am trying to force numlock to be on upon initial boot at the login screen on Ubuntu 12.04. The only solutions I have found so far switch numlock on only after initial login.  I'm looking to force numlock to be on when the login screen is displayed, and before the user has logged in. Can anyone assist? How do I set the desktop background on Windows from a script? On X Windows I had a cool 'silent-alarm" reminder script that would change my root window (background) color to solid red, just for a few seconds a few moments before changing it back. Is there a way to do this for Windows XP?  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Example top:  top - 12:43:48 up  3:02,  3 users,  load average: 6.57, 5.53, 3.33 Tasks: 256 total,   3 running, 253 sleeping,   0 stopped,   0 zombie %Cpu(s):  5.9 us, 16.6 sy,  0.0 ni, 74.7 id,  0.5 wa,  0.0 hi,  2.3 si,  0.0 st KiB Mem:   8080252 total,  7937856 used,   142396 free,   258904 buffers KiB Swap:        0 total,        0 used,        0 free.  4061336 cached Mem    PID USER      PR  NI    VIRT    RES    SHR S  %CPU %MEM     TIME+ COMMAND 13509 root     -51   0       0      0      0 S  54.7  0.0   3:29.47 kidle_inject/1 13511 root     -51   0       0      0      0 S  54.1  0.0   3:30.92 kidle_inject/3 13510 root     -51   0       0      0      0 S  48.8  0.0   3:11.60 kidle_inject/2 13508 root     -51   0       0      0      0 S  47.6  0.0   3:08.47 kidle_inject/0 computing the orbits for a group action Let $G$ be the Galois group of a field with nine elements over its subfield with three elements. 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