From: Stein A. Stromme (stromme@mi.uib.no)
Date: Sun Aug 03 2003 - 17:47:24 EDT
[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 :-)
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
This archive was generated by hypermail 2.1.4 : Sun Aug 03 2003 - 23:34:47 EDT