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.
Studying this equation can provide insight into the properties and behavior of prime numbers, which are fundamental building blocks in mathematics and have important applications in computer science and cryptography.
No, there is currently no proof that this equation always results in a prime number. It is a conjecture that has yet to be proven or disproven.
No, there are no known counterexamples. However, the fact that it has not been proven adds to the intrigue and mystery of this equation.
Yes, this equation can be rewritten as (p-1)(q-1)+1, which is known as the Euler's totient function. This function has been extensively studied and is closely related to prime numbers.
Yes, this equation plays a crucial role in the RSA algorithm, which is widely used for secure communication and data encryption. Understanding the properties of this equation can help in improving the security of RSA and other cryptographic systems.