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Math Help - twin primes

  1. #1
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    twin primes

    Ok so how would you quantify the statement that there is finite number of twin primes like using there exists, for all, free and bound variables. I know it is an open question but this is just hypothetical
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  2. #2
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    Quote Originally Posted by leinadwerdna View Post
    Ok so how would you quantify the statement that there is finite number of twin primes like using there exists, for all, free and bound variables. I know it is an open question but this is just hypothetical
    What about the following:
    Suppose our variables and constants are taken from the natural numbers and let P(n)\,,\,n\in\mathbb{N} be the statement "n is a prime number":

    \exists M\!\!\in\!\mathbb{N}\;\forall a\!\!\in\!\mathbb{N}\left(P(a)\wedge P(a+2)\rightarrow a<M\right)

    Tonio
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