[Haskell] Generator Function for Prime Numbers

[Thorkil Naur]

Hello,

On Tuesday 13 March 2007 00:40, Jacques Carette wrote:
> And yet Taral would be wrong and Dave Feustel correct:
> http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html
> 

I wouldn't say that a polynomium applies as "using only addition and 
subtraction".

> There is a polynomial (of degree 25) in 26 variables which generates 
> only primes whenever it is positive.  Surprising, yes it is.  Note that 
> this polynomial is actually rarely positive!
> 

Yes, and as noted in the Prime-GeneratingPolynomial reference, it is really a 
set of diophantine equations (equations where only integer/natural/rational 
solutions qualify) in disguise. In fact, if I remember correctly, one of the 
variables that you have to stick into the polynomium is one less (or some 
such) than the prime that you get out. So as a prime generating device, it is 
rather useless.

The idea of defining sets of numbers by diophantine equations was used in 
1970, to prove one of the 10th of Hilberts famous 23 problems from 1900 
impossible. See

  http://en.wikipedia.org/wiki/Matiyasevich's_theorem

> Jacques
> 
> Taral wrote:
> > Not bloody likely.
> >
> > On 3/12/07, Dave at haskell.org <Dave at haskell.org> wrote:
> >> I have heard that a generator function has been found that generates
> >> prime numbers directly using only addition and subtraction. There
> >> purportedly have been presentations of this information to selected
> >> mathematicians who have verified that the generator function works.
> >> But I haven't found any confirmation by googling. Has anyone got
> >> wind of this?
> >>
> >> Thanks,
> >> Dave Feustel
> >> _______________________________________________
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> >> Haskell at haskell.org
> >> http://www.haskell.org/mailman/listinfo/haskell
> >>
> >
> >
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Best regards
Thorkil