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Formula versus algorithm

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  • Kermit Rose
    To: Kermit Rose Subject: Re: Some philosophy about prime numbers ... From: JRenze Date: 12/19/05 18:21:19 Yes, I disagree. See
    Message 1 of 1 , Dec 20, 2005
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      To: Kermit Rose
      Subject: Re: Some philosophy about prime numbers

      --- In primenumbers@yahoogroups.com, "Kermit Rose" <kermit@p...> wrote:

      > "There is no formula that produces all primes and ONLY primes."
      >
      > Does anyone disagree with this statement?


      From: JRenze
      Date: 12/19/05 18:21:19

      Yes, I disagree. See http://functions.wolfram.com/13.03.06.0009.01 or
      http://mathworld.wolfram.com/PrimeFormulas.html Equations (13) and (14).

      This is a formula which for positive integer input n returns the nth
      prime. It is not recursive and no primes or number theoretic
      functions explicitly appear on the right hand side.

      John


      From Kermit Rose

      You show an interesting formula. It clearly shows that it's possible to
      cast a simple iterative algorithm

      into a formula by using the summation notation.

      Thus you show us that the summation notation blurs the distinction between
      a non-recursive algorithm and a
      simple formula.
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