- 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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Jetzt aktivieren unter http://www.gmx.net/info - 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] - Andreas Ernst wrote:
> Some people noted, that the url I gave was not

I'm sorry but your methods are well-known.

> 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'.

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