Re: loose ends

From: Stein A. Stromme (stromme@mi.uib.no)
Date: Sun Aug 03 2003 - 17:47:24 EDT

  • Next message: George Murphy: "Re: loose ends"

    [George Murphy]

    | Glenn Morton wrote:
    | >
    | > It isn't a new discovery but an old one, about 2500 years old. It is called
    | > the Primes Sieve of Eratosthenes. Given enough time, it will generate the
    | > entire list of primes. But that is the catch. It takes too much time.
    | >
    | > Look it up on the internet.
    |
    | Don't need to - I learned about it from Gamow's _One, Two,
    Three ... Infinity_
    | when I was about 14. It isn't a prime-generating formula but a device for
    | systematically checking to see if numbers are prime. By a proposed
    prime-generating
    | formula I mean something like
    | f(n) = n^2 - n + 41
    | which gives primes for n = 1, 2, ... 40 but for n = 41 gives a
    perfect square.

    George and Glenn,

    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 :-)

    SA

    -- 
    Stein Arild Str¯mme            +47 55584825, +47 95801887
    Universitetet i Bergen                  Fax: +47 55589672
    Matematisk institutt               www.mi.uib.no/stromme/
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