- Jack Brennen wrote:
>

No, it cannot.

> Indeed, the prime of the form k+2^n might be in the covering set for

> the numbers of the form k*2^n+1.

>

The covering sets of all known Riesel and Sierpinski numbers are

exactly the same as that of their duals, as can be easily seen.

So if a prime for a dual of a Sierpinski number were to be in the

covering set of that particular Sierpinski number, it should also be

in the dual covering set as well, which contradicts the definition of

covering sets.

Lélio - --- On Mon, 5/19/08, Lélio Ribeiro de Paula <lelio73@...> wrote:
> Jack Brennen wrote:

Now reread what Jack wrote (which was also going be in my original post too, but thinking that it was a bit obvious I removed it for brevity), and think a bit more.

> > Indeed, the prime of the form k+2^n might be in the

> covering set for

> > the numbers of the form k*2^n+1.

>

> No, it cannot.

>

> The covering sets of all known Riesel and Sierpinski

> numbers are

> exactly the same as that of their duals, as can be easily

> seen.

>

> So if a prime for a dual of a Sierpinski number were to be

> in the

> covering set of that particular Sierpinski number, it

> should also be

> in the dual covering set as well, which contradicts the

> definition of

> covering sets.

Phil - Phil Carmody wrote:
>

I tried (in private email) giving the example of the dual sequences:

> Now reread what Jack wrote (which was also going be in my original post too, but thinking that it was a bit obvious I removed it for brevity), and think a bit more.

>

10^n-7

7*10^n-1

They both have the same covering set (it can be found in under a

minute with just a little thought). One of the sequences has a

very easy to find prime; the other one is easily proven to have no

primes.