From: George Murphy (gmurphy@raex.com)
Date: Sun Aug 03 2003 - 14:03:47 EDT
Glenn Morton wrote:
>
> >-----Original Message-----
> >From: George Murphy [mailto:gmurphy@raex.com]
> >Sent: Saturday, August 02, 2003 9:04 PM
> >To: Glenn Morton
>
> > There is a basic difference between the Fibonacci sequence
> >& the primes. As you
> >note, there is a formula with which one can generate as many
> >members of the 1st sequence
> >as you wish. But there is no general formula for generating
> >primes (unless there's been
> >a new discovery I haven't heard of, a possibility since I'm hardly
> >a number theorist).
> >All proposed prime-generating formulas have been found to break
> >down at some point.
>
> 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.
Shalom,
George
George L. Murphy
gmurphy@raex.com
http://web.raex.com/~gmurphy/
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