Re: loose ends

From: Stein A. Stromme (stromme@mi.uib.no)
Date: Mon Aug 04 2003 - 02:37:26 EDT

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    [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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