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

  • #1

Homework Statement


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

Homework Equations


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

The Attempt at a Solution


I tried to find online a formula that would justify this, but was unable to find anything.
 

Answers and Replies

  • #2
Nathanael
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Why does (p*q+2)-(p+q) always give a prime number when p and q are prime?
It doesn't.

The first example I picked was a counter example:
(17*47+2)-(17+47)=737=11*67
 
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  • #3
It doesn't.

The first example I picked was a counter example:
(17*47+2)-(17+47)=737=11*67
Oh you're right. I should have tried more examples. Thank you
 
  • #4
haruspex
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Oh you're right. I should have tried more examples. Thank you
You couldn't have tried many. It fails whenever p and q differ by 2.
 
  • #5
You couldn't have tried many. It fails whenever p and q differ by 2.
I tried 7 and 13
 
  • #7
phinds
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I tried 7 and 13
And you think one example is enough to generalize from ? Probably not a great idea.
 
  • #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.
 
  • #9
phinds
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Gez no I tried 3 examples 3,7 1,3 7,13, and it would have made sense with the problem I'm doing.
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.
 
  • #10
vela
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Gez no I tried 3 examples 3,7 1,3 7,13, and it would have made sense with the problem I'm doing.
Your second example isn't valid because 1 isn't a prime number.
 

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