The expression (p*q+2)-(p+q) does not consistently yield a prime number when both p and q are prime. A counterexample provided is (17*47+2)-(17+47)=737, which factors into 11*67, demonstrating that the formula fails. Additionally, the discussion highlights that the expression fails when p and q differ by 2, as shown by attempts with pairs like (3, 5) and (7, 13). The conclusion is that this expression cannot be relied upon to generate prime numbers.
PREREQUISITESMathematics students, educators, and anyone interested in number theory and the properties of prime numbers.
It doesn't.John Harris said:Why does (p*q+2)-(p+q) always give a prime number when p and q are prime?
Oh you're right. I should have tried more examples. Thank youNathanael said:It doesn't.
The first example I picked was a counter example:
(17*47+2)-(17+47)=737=11*67
You couldn't have tried many. It fails whenever p and q differ by 2.John Harris said:Oh you're right. I should have tried more examples. Thank you
I tried 7 and 13haruspex said:You couldn't have tried many. It fails whenever p and q differ by 2.
Only that pair?! Try 3 and 5, 5 and 7, 11 and 13,...John Harris said:I tried 7 and 13
And you think one example is enough to generalize from ? Probably not a great idea.John Harris said:I tried 7 and 13
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.John Harris said: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.John Harris said:Gez no I tried 3 examples 3,7 1,3 7,13, and it would have made sense with the problem I'm doing.