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17476Prime generating polynomials contest

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  • ed pegg
    Jan 2, 2006
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      The next Al Zimmermann Programming contest might be about
      Prime Generating Polynomials. It's currently running neck
      and neck with Protein Folding.

      Under the rules I'm proposing for the contest, here are the
      current known record holders for Prime Generating Polynomials,
      orders 1 to 4. Orders 5 and up seem to be unexplored.

      1) 44546738095860 n + 56211383760397 Score:23 n=0..22 Frind
      2) 36 n^2 - 810 n + 2753 Score:45 n=0..44 Ruby
      3) 3 n^3 - 183 n^2 + 3318 n - 18757 Score:43 n=0..46 Ruiz
      4) n^4 + 29 n^2 + 101 Score:20 n=0..19 Pegg

      The scoring rules:
      1. Polynomial f(k) must produce primes from 0 to n.
      2. The score will be the number of *distinct* primes
      when |f(k)| is evaluated from 0 to n.
      3. In case of a tie, the lower value (tighter value) of n wins.
      4. In case of a tie, the product of non-zero coefficients will
      be evaluated, and the lowest product wins.

      My own result for order-4 polynomials will likely be surpassed
      very easily. If you would like to vote for this contest, please
      visit http://www.recmath.com/contest/ . The winners will split
      up $500.

      Ed Pegg Jr
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