RE twin primes conjecture: A property of twin primes, only?

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Jose RamÃ³n Brox

... From: Kermit Rose ... No, it s not! You are forgetting the first line of the conjecture. I will restate it: KNOWING that p and q are

Message 1 of 1
, Jul 5, 2006

----- 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
>> integer.

>sqrt([ (23^2 + 25^2)/2 -1)
>= sqrt(529 + 625)/2 - 1)
>= sqrt(1154/2 -1)
>=sqrt(577 - 1)
>= sqrt(576)
>= 24
>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

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