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## consecutive twin primes

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• 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
Message 1 of 4 , May 31, 2001
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,
Message 2 of 4 , May 31, 2001
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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• 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
Message 3 of 4 , Jun 1, 2001
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
> ---------------------------------------------------
> ����� ����������� ����� �� ������! ��� �����,
> ���������� � ��������.
> ���������������. ������ ������������. ������
> ���������, ����������
> �� ������ ����...
> ��������� ������-�����, ��� (017) 226-56-73,
> 220-86-71
>
> Unsubscribe by an email to:
> primenumbers-unsubscribe@egroups.com
> The Prime Pages : http://www.primepages.org
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>
>
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• Hello! ... There are 7 chains of 8 consecutive twins below 10^13, found by Denis DeVries. This is a copy of his message sent on ... From: Denis DeVries
Message 4 of 4 , Jun 1, 2001
Hello!

Bouk de wrote:

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

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