17476Prime generating polynomials contest
- Jan 2, 2006The 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
Ed Pegg Jr
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