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13944Re: [PrimeNumbers] Infinite primes-> a Turing Machine prime sieve that never stops?

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  • Nathan Russell
    Nov 3, 2003
      --On Monday, November 03, 2003 10:32 PM -0500 Jud McCranie <j.mccranie@...> wrote:

      >
      >>> 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.

      Equally, there are infinitely many integers, or even numbers, but there is no one infinite integer - it is simply the case that for any integer n, you can find a successor n+1 which is also an integer.

      Every prime also has a successor - there is no largest prime (whereas there IS a largest member of any finite set, for example there is a tallest person in the world, or a smallest planet in the solar system). However, since primes are defined as being a subset of the positive integers, there is no infinite prime.

      Does that make sense, Roger?

      Regards,
      Nathan
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