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

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  • Phil Carmody
    ... 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 3:59 AM
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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
    • Jack Brennen
      ... 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 7:40 AM
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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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