The discussion revolves around the expression (p*q+2)-(p+q) and its relationship to prime numbers when p and q are prime. Participants explore whether this expression always yields a prime number and inquire about similar formulas.
The discussion is active, with participants sharing examples and counterexamples. There is recognition of the need for more thorough testing of the expression with various prime pairs, and some guidance is offered regarding the validity of examples used.
Participants note that the expression fails under specific conditions, such as when p and q differ by 2. There is also a mention of the importance of using valid prime numbers in examples, as one participant incorrectly included 1 as a prime.
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.