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Why does (p*q+2)-(p+q) always give a prime number?

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  1. Feb 10, 2015 #1
    1. The problem statement, all variables and given/known data
    Why does (p*q+2)-(p+q) always give a prime number when p and q are prime? Is there a similar formula that would prove this

    2. Relevant equations
    That's what I'm looking for. It might have something to do with Eulers formula

    3. The attempt at a solution
    I tried to find online a formula that would justify this, but was unable to find anything.
     
  2. jcsd
  3. Feb 10, 2015 #2

    Nathanael

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    It doesn't.

    The first example I picked was a counter example:
    (17*47+2)-(17+47)=737=11*67
     
  4. Feb 10, 2015 #3
    Oh you're right. I should have tried more examples. Thank you
     
  5. Feb 10, 2015 #4

    haruspex

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    You couldn't have tried many. It fails whenever p and q differ by 2.
     
  6. Feb 10, 2015 #5
    I tried 7 and 13
     
  7. Feb 10, 2015 #6

    haruspex

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    Only that pair?! Try 3 and 5, 5 and 7, 11 and 13,.....
     
  8. Feb 10, 2015 #7

    phinds

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    And you think one example is enough to generalize from ? Probably not a great idea.
     
  9. Feb 10, 2015 #8
    Gez no I tried 3 examples 3,7 1,3 7,13, and it would have made sense with the problem I'm doing.
     
  10. Feb 11, 2015 #9

    phinds

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    Well can you see how your statement "I tried 7 and 13" sounds a LOT like "I tried one combination" ? Glad to hear you already realize that just one is not a good idea.
     
  11. Feb 12, 2015 #10

    vela

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    Your second example isn't valid because 1 isn't a prime number.
     
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