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14972Re: [PrimeNumbers] Sieve for twin primes

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  • Jens Kruse Andersen
    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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