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Re: [PrimeNumbers] Primaliy test for a series

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  • Christ van Willegen
    ... ...except for 3, 7, and loads of other Mersenne numbers? Christ van Willegen
    Message 1 of 7 , Feb 21, 2007
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      On 2/21/07, Phil Carmody <thefatphil@...> wrote:
      > --- plesala <plesala@...> wrote:
      > > Hi to all,
      > >
      > > How does one test primality of a series like
      > >
      > > 1 + 2 + 2^2 + 2^3 + ... + 2^(2*n - 1),
      > >
      > > for example, using primeform?
      >
      > It's the sum of a geometric progression, so has a closed form representation.
      > Just test that closed form instead. However, I think you won't find any
      > primes in that series.

      ...except for 3, 7, and loads of other Mersenne numbers?

      Christ van Willegen
    • Andrey Kulsha
      ... No, only except for 3. All of them are divisible by 3. :) [Non-text portions of this message have been removed]
      Message 2 of 7 , Feb 21, 2007
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        > > > How does one test primality of a series like
        > > >
        > > > 1 + 2 + 2^2 + 2^3 + ... + 2^(2*n - 1),
        > > >
        > > > for example, using primeform?
        > >
        > > It's the sum of a geometric progression, so has a closed form representation.
        > > Just test that closed form instead. However, I think you won't find any
        > > primes in that series.
        >
        > ...except for 3, 7, and loads of other Mersenne numbers?

        No, only except for 3. All of them are divisible by 3. :)

        [Non-text portions of this message have been removed]
      • Phil Carmody
        ... I can t get that expression to sum to 7, 31, 127, ... Phil () ASCII ribbon campaign () Hopeless ribbon campaign / against HTML mail /
        Message 3 of 7 , Feb 21, 2007
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          --- Christ van Willegen <cvwillegen@...> wrote:
          > On 2/21/07, Phil Carmody <thefatphil@...> wrote:
          > > --- plesala <plesala@...> wrote:
          > > > Hi to all,
          > > >
          > > > How does one test primality of a series like
          > > >
          > > > 1 + 2 + 2^2 + 2^3 + ... + 2^(2*n - 1),
          > > >
          > > > for example, using primeform?
          > >
          > > It's the sum of a geometric progression, so has a closed form
          > representation.
          > > Just test that closed form instead. However, I think you won't find any
          > > primes in that series.
          >
          > ...except for 3, 7, and loads of other Mersenne numbers?

          I can't get that expression to sum to 7, 31, 127, ...

          Phil

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        • Thomas Hadley
          The original series is not specified correctly. The last term implies that all exponents must be odd, yet the first and third exponents are even. ... Since we
          Message 4 of 7 , Feb 21, 2007
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            The original series is not specified correctly.
            The last term implies that all exponents must be
            odd, yet the first and third exponents are even.
            >
            > 1 + 2 + 2^2 + 2^3 + ... + 2^(2*n - 1),
            >
            Since we don't know what the original poster
            intended, we can't really answer his question.

            Tom Hadley
          • plesala
            Pardon for the clumsy statement I made. Of course the summation I give is easy to simplify. Actually my interest is summations that are slightly more
            Message 5 of 7 , Feb 22, 2007
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              Pardon for the clumsy statement I made. Of course the summation I give is easy to simplify. Actually my interest is summations that are slightly more complicated.

              Whenever I try to search for primes of the form
              6*n*(2^p - 1- n) + 2^p - 1, where n = 1, 2, 3, ... and 2^p - 1 is a Mersenne prime, I find that the factors are of the form

              2^(3*k) - 1 = (2^3 - 1)( (2^3)^(k - 1) + (2^3)^k - 2) + ...
              (2^3)^2 + (2^3) + 1),

              or alternatively

              2^(3*k) + 1 = (2^3 + 1)( (2^3)^(k - 1) - (2^3)^(k - 2) + ...
              + (2^3)^2 - (2^3) + 1), where k is odd.

              I wonder whether some of these factor summations cannot yield fairly large primes.

              Peter.
              ----- Original Message -----
              From: plesala
              To: primenumbers@yahoogroups.com
              Sent: Wednesday, February 21, 2007 1:54 PM
              Subject: [PrimeNumbers] Primaliy test for a series


              Hi to all,

              How does one test primality of a series like

              1 + 2 + 2^2 + 2^3 + ... + 2^(2*n - 1),

              for example, using primeform?

              Thank you.
              Peter.




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