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13943Re: [PrimeNumbers] Infinite primes-> a Turing Machine prime sieve that never stops?

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  • Jud McCranie
    Nov 3, 2003
      >>At 12:51 PM 11/2/2003 -0800, Roger Bagula wrote:
      >> >It is reasonable to assume that an infinite prime might exist ,
      >>>but could never be computed.

      It is not reasonable to assume that. Are you assuming that because there
      are an infinite number of prime numbers that one of them is infinite? That
      is false. There are an infinite number of primes, but each of them is finite.

      Also, there is a proof "Every Prime has a succinct certificate", by Vaughn
      Pratt IIRC, which says that every prime can be proven so in a finite number
      of steps/time.
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