From: Stein A. Stromme (stromme@mi.uib.no)
Date: Mon Aug 04 2003 - 02:37:26 EDT
[George Murphy]
| Stein A. Stromme wrote:
| >
| > Actually, there exist a polynomial with integer coefficients in 10
| > variables such that the _positive_ values obtained as values of the
| > polynomial at integer values of the variables are exactly all primes.
| >
| > See e.g.
| >
| > <http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html>.
| >
| > Not that it matters much, though :-)
|
| Does this actually give _all_ primes? If so I stand corrected.
It does, but note the qualification of positiveness. By far most
values are negative, and the polynomial cannot be used to _enumerate_
the primes, like generating them in increasing order for example;
for that the sieve is much simpler.
SA
-- Stein Arild Str¯mme +47 55584825, +47 95801887 Universitetet i Bergen Fax: +47 55589672 Matematisk institutt www.mi.uib.no/stromme/ Johs Brunsg 12, N-5008 BERGEN stromme@mi.uib.no
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