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