Re: loose ends

From: George Murphy (gmurphy@raex.com)
Date: Mon Aug 04 2003 - 00:17:55 EDT

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    Stein A. Stromme wrote:
    >
    > [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 :-)

            Does this actually give _all_ primes? If so I stand corrected.
                                                                    George

    George L. Murphy
    gmurphy@raex.com
    http://web.raex.com/~gmurphy/



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