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Re: [PrimeNumbers] Twin primes was: Infinite primes

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  • liufs
    ... So there a contradiction, and the number of primes is infinite. It is not to say that indeed q and r both are prime , otherwise, you wold prove the twin
    Message 1 of 3 , Mar 31 12:55 AM
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      David Litchfield <Mnemonix@...>wrote:


      > Yep. The reason I ask was because this could prove the twin prime
      > conjecture.
      >
      > If q= P1 * P2 * ... Pn + 1
      >
      > then q is prime because q mod and Pn is 1.
      > Using the same logic, it also follows that
      >
      > r = P1 * P2 * .... Pn -1
      >
      > is also prime because r mod any Pn equals Pn-1


      So there a contradiction, and the number of primes is infinite.
      It is not to say that indeed q and r both are prime , otherwise, you wold
      prove the twin prime conjecture


      > q - r = 2.

      > That said in _reality_ q and r could both be composite - with two or more
      > primes not in P1 to Pn being the factors. But then this is confusing reality
      > with a hypothetical situtation so does this proof for the twin prime
      > conjecture stand in the same way the Euclid's proof is accepted. At best
      > this proves the twin prime conjecture - at worst it proves at least the
      > possibility of an infinite number of twin primes.


      But then this is not confusing reality with a hypothetical situtation , it is you are
      confusing your logic.

      Liu Fengsui
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