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Sieve for twin primes

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  • Andreas Ernst
    Hi: I found a simple sieve method, somewhat similar to the sieve of Erathostenes, which allows to directly sieve twin primes. I would like to know, if this
    Message 1 of 3 , Jun 10, 2004
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      Hi:

      I found a simple sieve method, somewhat similar
      to the sieve of Erathostenes, which allows to directly
      sieve twin primes. I would like to know, if this method
      is already known in the literature and if a proof for
      it exists.

      You can find the ps file under the url:

      http://www.rzuser.uni-heidelberg.de/~aernst/sieve1.ps

      Andreas


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    • Andreas Ernst
      Hi again: Some people noted, that the url I gave was not valid. Please try to access the ps file on a sieve for twin primes via my homepage
      Message 2 of 3 , Jun 12, 2004
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        Hi again:

        Some people noted, that the url I gave was not
        valid. Please try to access the ps file on a sieve
        for twin primes via my homepage

        http://www.rzuser.uni-heidelberg.de/~aernst

        You find the ps file in the section 'Hobbies'.

        Thanks, Andreas



        > Hi:
        >
        > I found a simple sieve method, somewhat similar
        > to the sieve of Erathostenes, which allows to directly
        > sieve twin primes. I would like to know, if this method
        > is already known in the literature and if a proof for
        > it exists.
        >
        > You can find the ps file under the url:
        >
        > http://www.rzuser.uni-heidelberg.de/~aernst/sieve1.ps
        >
        > Andreas



        --
        "Sie haben neue Mails!" - Die GMX Toolbar informiert Sie beim Surfen!
        Jetzt aktivieren unter http://www.gmx.net/info

        [Non-text portions of this message have been removed]
      • Jens Kruse Andersen
        ... I m sorry but your methods are well-known. All primes above 3 are on the form 6n+/-1. You use this with a wheel of size 6 to avoid numbers divisible by 2
        Message 3 of 3 , Jun 12, 2004
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          Andreas Ernst wrote:
          > Some people noted, that the url I gave was not
          > valid. Please try to access the ps file on a sieve
          > for twin primes via my homepage
          >
          > http://www.rzuser.uni-heidelberg.de/~aernst
          >
          > You find the ps file in the section 'Hobbies'.

          I'm sorry but your methods are well-known.
          All primes above 3 are on the form 6n+/-1. You use this with a wheel of size 6
          to avoid numbers divisible by 2 or 3. That is common. Larger wheels, e.g. of
          size 5# = 30 to also avoid numbers divisible by 5, are more efficient in many
          cases.
          Your second idea is to represent the potential twin 6n+/-1 with a single bit
          representing n instead of 2 bits, one for each of the 2 numbers. This is also a
          very common technique when searching a set of 2 or more simultaneous primes. If
          a set of m primes is required, m=2 for twin primes, then each sieve prime p runs
          through m loops to strike out n for which the i'th number (1<=i<=m) in the m-set
          is divisible by p.

          --
          Jens Kruse Andersen
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