## Re: [PrimeNumbers] Re: Proving Sierpinski conjecture before SoB completes its task

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• ... 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
Message 1 of 7 , May 19, 2008
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--- On Mon, 5/19/08, LĂ©lio Ribeiro de Paula <lelio73@...> wrote:
> Jack Brennen wrote:
> > 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.

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.

Phil
• ... I tried (in private email) giving the example of the dual sequences: 10^n-7 7*10^n-1 They both have the same covering set (it can be found in under a
Message 2 of 7 , May 19, 2008
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Phil Carmody 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.
>

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

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.
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