Indeed,the non-existence of a finite covering set does

not prove infinite number of primes.Some time ago i

had constructed a "possible"-infinite covering set for

the Sierpinski numbers which used the algebraic

factoring of 4*X^4+1.

--- Jens Kruse Andersen <

jens.k.a@...> wrote:

> Thomas wrote:

>

> > What do you think, does there exist a base b such

> that n*b^n-1 or

> > n*b^n+1 never is prime?

> >

> > I have no answer to that question, but maybe it is

> easy for some of

> > you to create such a base b, so that n*b^n +1/-1

> always have small

> > factors.

>

> No base b has a finite covering set of factors.

> If M is a finite set then let A be the product of

> the members.

> If n=k*A for any k, then n*b^n+/-1 clearly never has

> a factor in M.

>

> This does not necessarily mean there always is a

> prime.

> There could be an algebraic factor I have

> overlooked. I know little about that.

> If there is not then heuristics seem to support

> infinitely many primes for all

> b.

>

> --

> Jens Kruse Andersen

>

>

__________________________________

Do you Yahoo!?

Yahoo! Search - Find what you�re looking for faster

http://search.yahoo.com