Re: loose ends

From: Stein A. Stromme (stromme@mi.uib.no)
Date: Mon Aug 04 2003 - 08:22:30 EDT

  • Next message: Stein A. Stromme: "Re: loose ends"

    [George Murphy]

    | I'm surprised. With my meager knowledge of number theory I
    | can sort of see how one might show that the positive values are
    | _only_ primes, but not how one could show that this generates _all_
    | primes. I hope that sometime in this life I'll be able to follow
    | this up in more detail. But that's kind of like wishing I had time
    | to learn Italian well enough to read the Divine Comedy. Eventually
    | you reach a point where you realize it ain't gonna happen.

    Here's a better reference, where you can actually see the polynomial,
    although this is has 26 variables rather than 10:

                <http://www.bath.ac.uk/~ensab/Primes/>.

    Note its very special form: it is (k+2) times something which is
    positive only if it is equal to 1, if and only if a whole bunch of
    squares are zero. Hence it is a set of diophantine equations in
    disguise, and together they form a criterion for k+2 to be prime.

    I was wrong to say that the arguments were to take arbitrary integer
    values; that should have been arbitrary non-negative integer values
    instead.

    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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