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

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  • Jose Ramón 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
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      ----- 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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