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

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1. Feb 10, 2015

### John Harris

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. Feb 10, 2015

### Nathanael

It doesn't.

The first example I picked was a counter example:
(17*47+2)-(17+47)=737=11*67

3. Feb 10, 2015

### John Harris

Oh you're right. I should have tried more examples. Thank you

4. Feb 10, 2015

### haruspex

You couldn't have tried many. It fails whenever p and q differ by 2.

5. Feb 10, 2015

### John Harris

I tried 7 and 13

6. Feb 10, 2015

### haruspex

Only that pair?! Try 3 and 5, 5 and 7, 11 and 13,.....

7. Feb 10, 2015

### phinds

And you think one example is enough to generalize from ? Probably not a great idea.

8. Feb 10, 2015

### John Harris

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. Feb 11, 2015

### phinds

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. Feb 12, 2015

### vela

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

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