At 07:51 PM 11/13/98 -0800, William Stuart wrote:
>Another interesting thing about this conjecture...
>
>If it is correct, then there is no last prime.
There's no last prime anyways. This is Euclid's Theorem and was proven
thousands of years ago, as follows:
Let p1, p2, ... , pn be a finite collection of primes. Let N = (p1p2...pn)
+ 1. Now N is clearly not divisible by any of the primes. If N is prime,
then it is a prime not in the list. If N is not prime, it can be factored
as N1N2, neither of which is divisible by any of the ps; and both strictly
smaller than N; so eventually by this process you must find a prime factor
of N that is not in the collection. Hence any finite collection of primes
is incomplete, hence there must be infinitely many primes.
--
.*. "Clouds are not spheres, mountains are not cones, coastlines are not
-() < circles, and bark is not smooth, nor does lightning travel in a
`*' straight line." -------------------------------------------------
-- B. Mandelbrot |http://surf.to/pgd.net
_____________________ ____|________ Paul Derbyshire [EMAIL PROTECTED]
Programmer & Humanist|ICQ: 10423848|
