- A number of us have been searching for nine consecutive twin primes. Consecutive meaning that there are no isolated single primes among the "constellation".

Is it possible (probable) that none exist?

I don't think the Hardy-Littlewood conjecture covers this case.

Jim Morton

[Non-text portions of this message have been removed] - I think that such a chain exists. Heuristically there are

infinite number of them.

For example, numbers

p+(0, 2, 12, 14, 30, 32, 42, 44, 72, 74, 78, 80, 108, 110,

120, 122, 150, 152)

may be 18 consecutive primes infinitely many times

(heuristically).

Andrey

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бЗЕОФУФЧП демйху-феттб, ФЕМ (017) 226-56-73, 220-86-71 - I am also confinced that such a chain is possible. It

will be extremely rare though.

You might want to check out:

http://www.ltkz.demon.co.uk/ktuplets.htm

A site which records record k-tuplet primes which is

not unlike your search for consecutive twins.

For example:

2845372542509911868266807 + 0, 4, 10, 12, 16, 22, 24,

30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70 (25 digits,

2000, Joerg Waldvogel & Peter Leikauf)

is the record 18-tuplet.

You haven't made it easy for yourself with 9

consecutive twins though;-)

Have you found lesser chains already? Say 3 or 4

consecutive twins?

Bouk.

--- Andrey Kulsha <Andrey_601@...> wrote:> I think that such a chain exists. Heuristically

__________________________________________________

> there are

> infinite number of them.

>

> For example, numbers

>

> p+(0, 2, 12, 14, 30, 32, 42, 44, 72, 74, 78, 80,

> 108, 110,

> 120, 122, 150, 152)

>

> may be 18 consecutive primes infinitely many times

> (heuristically).

>

> Andrey

> ---------------------------------------------------

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a year! http://personal.mail.yahoo.com/ - Hello!

Bouk de wrote:

>Have you found lesser chains already? Say 3 or 4

There are 7 chains of 8 consecutive twins below 10^13, found

>consecutive twins?

by Denis DeVries. This is a copy of his message sent on

NMBRTHRY list:

----- Original Message -----

From: Denis DeVries <ddevries2@...>

To: <NMBRTHRY@...>

Sent: Thursday, May 31, 2001 4:58 PM

Subject: Twin Prime Groups

> I've completed an exhaustive search of all primes through

10^13 & found

> seven sets of eight consecutive twin primes. There are no

sets of nine

> consecutive twins < 10^13.

>

> the seven "eight clusters" or "Octa-primes" are:

>

> 110 78197 32821 - 33063

> 373 52832 49697 - 49963

> 458 86461 46631 - 46813

> 634 06985 79419 - 79619

> 841 26497 48537 - 48689

> 920 63598 43907 - 44179

> 966 71456 61911 - 62129

>

> I'd be interested in hearing of the first discovery of a

set of nine

> consecutive twins.

>

> Denis DeVries

> dhdevries@...

----------------------

I guess that Jim Morton read this message and then asked our

PrimeNumbers list about this problem (9 consecutive twins).

Best wishes,

Andrey

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