RE twin primes conjecture: A property of twin primes, only?
----- Original Message -----
From: "Kermit Rose" <kermit@...>
>> Let p q consecutive prime numbers p<q.
>> Let z=sqrt[(p^2+q^2)/2-1]
>> Conjecture: p&q ares twin primes IF AND ONLY IF z is
>sqrt([ (23^2 + 25^2)/2 -1)
>= sqrt(529 + 625)/2 - 1)
>= sqrt(1154/2 -1)
>=sqrt(577 - 1)
>Is this a counter example to the if part?
No, it's not! You are forgetting the first line of the conjecture. I will restate it:
KNOWING that p and q are consecutive prime numbers with p < q, then p and q are twins iff
z=sqrt(p^2+q^2)/2-1) is integer.
Your counterexample isn't valid, since it doesn't fulfill the first condition: 23 and 25
they aren't consecutive primes!
You can look at it in another way: you select a prime number, and scan for the next one;
if you compute z and it's an integer, can you conclude that q-p = 2?
Regards. Jose Brox