From: George Murphy (gmurphy@raex.com)
Date: Mon Aug 04 2003 - 00:17:55 EDT
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/
This archive was generated by hypermail 2.1.4 : Mon Aug 04 2003 - 00:16:33 EDT