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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.
      http://www.recmath.com/contest/votes.php

      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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