## New 18-tuplet

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• I have just found 3rd known (the largest known) prime 18-tuplet: Prime 18-tuplet 4530085223434265844952597 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42,
Message 1 of 14 , Dec 13 8:56 PM
I have just found 3rd known (the largest known) prime 18-tuplet:

Prime 18-tuplet
4530085223434265844952597 + d,
d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
(25 digits, Dec 14, 2008, Jaroslaw Wroblewski)

The search has started on December 4. I am using up to 60 64-bit
computers in students labs at Mathematical Institute of Wroclaw
University (sometimes fewer if the are down or used by students).

I estimate that I have deserved to find about 0.5-0.6 of an 18-tuplet
by now, so I was a bit lucky. I will continue the search in hope for
more 18-tuplets or for a miracle (19-tuplet).

Jarek
• ... Congratulations on another impressive record! You now have all records for 15 to 21 simultaneous primes at http://hjem.get2net.dk/jka/math/simultprime.htm
Message 2 of 14 , Dec 14 8:35 AM
Jarek wrote:
> I have just found 3rd known (the largest known) prime 18-tuplet:
> 4530085223434265844952597 + d,
> d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
> (25 digits, Dec 14, 2008, Jaroslaw Wroblewski)

Congratulations on another impressive record!
You now have all records for 15 to 21 simultaneous primes at
http://hjem.get2net.dk/jka/math/simultprime.htm

It is actually the 4th known 18-tuplet including a trivial from 13 to 83.
There are also trivial 19- to 23-tuplets with primes below 120.
The first size with no known example is a 24-tuplet which I guess
even you will not find for many years.

--
Jens Kruse Andersen
• ... Congratulations! It always amazes me to see primes at those densities at such large numbers. I wonder if future quantum computers (if such really are
Message 3 of 14 , Dec 16 6:49 AM
--- In primenumbers@yahoogroups.com, "jarek372000" <jaroslaw.wroblewski@...> wrote:
>
> I have just found 3rd known (the largest known) prime 18-tuplet:
>
> Prime 18-tuplet
> 4530085223434265844952597 + d,
> d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
> (25 digits, Dec 14, 2008, Jaroslaw Wroblewski)
>

Congratulations! It always amazes me to see primes at those densities at such 'large'
numbers. I wonder if future quantum computers (if such really are possible) would be able to
find the yet unfound, probably monstrously sized 24 tuplets that Jens alluded to.

Mark
• I just got another 18-tuplet: Prime 18-tuplet 11298510058634407483251313 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26
Message 4 of 14 , Dec 17 9:06 PM
I just got another 18-tuplet:

Prime 18-tuplet
11298510058634407483251313 + d,
d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
(26 digits, Dec 18, 2008, Jaroslaw Wroblewski)

Jarek
• I just got another 18-tuplet: Prime 18-tuplet 23531820918273007548405133 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26
Message 5 of 14 , Jan 15, 2009
I just got another 18-tuplet:

Prime 18-tuplet
23531820918273007548405133 + d,
d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
(26 digits, Jan 2009, Jaroslaw Wroblewski)

Jarek
• I just got another prime 18-tuplet: 33755528632220819791319947 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70 (26 digits, Jan
Message 6 of 14 , Jan 25, 2009
I just got another prime 18-tuplet:

33755528632220819791319947 + d,
d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
(26 digits, Jan 26, 2009, Jaroslaw Wroblewski)

This is the largest known 18-tuplet and the largest known case of 18
Simultaneous Primes.

Jarek
• ... Congratulations! My ISP was bought and the buyer closed the old webhost last week. My former site at http://hjem.get2net.dk/jka has moved to
Message 7 of 14 , Jan 26, 2009
Jarek wrote:
> 33755528632220819791319947 + d,
> d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
> (26 digits, Jan 26, 2009, Jaroslaw Wroblewski)
>
> This is the largest known 18-tuplet and the largest known case of 18
> Simultaneous Primes.

and then:
> Here is the new AP19 with the smallest known start.
>
> 275525353 + 407133393*19#*n, n=0,..,18
> (Mariusz Szafranski, BOINC@Poland, Jaroslaw Wroblewski)

Congratulations!

My ISP was bought and the buyer closed the old webhost last week.
My former site at http://hjem.get2net.dk/jka has moved to
http://users.cybercity.dk/~dsl522332
File names are unchanged so all url's must just replace the start.
My email is unchanged.
The Largest Known Simultaneous Primes are now at
http://users.cybercity.dk/~dsl522332/math/simultprime.htm
Primes in Arithmetic Progression Records are at
http://users.cybercity.dk/~dsl522332/math/aprecords.htm
The pages are updated.

--
Jens Kruse Andersen
• I just got another prime 18-tuplet: 44453357465442632103684223 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26 digits, Feb 20,
Message 8 of 14 , Feb 19, 2009
I just got another prime 18-tuplet:

44453357465442632103684223 + d,
d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
(26 digits, Feb 20, 2009, Jaroslaw Wroblewski)

This is the largest known 18-tuplet and the largest known case of 18
Simultaneous Primes.

Jarek
• ... Congratulations! An 18-tuplet is very impressive and this is your fifth. http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated. -- Jens
Message 9 of 14 , Feb 20, 2009
Jarek wrote:
> 44453357465442632103684223 + d,
> d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
> (26 digits, Feb 20, 2009, Jaroslaw Wroblewski)
>
> This is the largest known 18-tuplet and the largest known case of 18
> Simultaneous Primes.

Congratulations!
An 18-tuplet is very impressive and this is your fifth.
http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated.

--
Jens Kruse Andersen
• I just got another prime 18-tuplet: 51342365971531191697537333 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26 digits, Mar 11,
Message 10 of 14 , Mar 11, 2009
I just got another prime 18-tuplet:

51342365971531191697537333 + d,
d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
(26 digits, Mar 11, 2009, Jaroslaw Wroblewski)

This is the largest known 18-tuplet and the largest known case of 18
Simultaneous Primes.

Jarek
• I have just discovered the first known 27-digit prime 18-tuplet: 159272023128204753638724847 + d, d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60,
Message 11 of 14 , Jan 15, 2010
I have just discovered the first known 27-digit prime 18-tuplet:

159272023128204753638724847 + d,
d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
(27 digits, Jan 15, 2010, Jaroslaw Wroblewski)

This is the largest known 18-tuplet and the largest known case of 18
Simultaneous Primes.

Jarek
• ... Congratulations! http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated with your 7th 18-tuplet record. -- Jens Kruse Andersen
Message 12 of 14 , Jan 15, 2010
Jaroslaw Wroblewski wrote:
> 159272023128204753638724847 + d,
> d = 0, 4, 10, 12, 16, 22, 24, 30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70
> (27 digits, Jan 15, 2010, Jaroslaw Wroblewski)
>
> This is the largest known 18-tuplet and the largest known case of 18
> Simultaneous Primes.

Congratulations!
http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated

--
Jens Kruse Andersen
• I have just discovered another 27-digit prime 18-tuplet: Prime 18-tuplet 183837276562811649018077773 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48,
Message 13 of 14 , Apr 25, 2010
I have just discovered another 27-digit prime 18-tuplet:

Prime 18-tuplet
183837276562811649018077773 + d,
d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
(27 digits, Apr 26, 2010, Jaroslaw Wroblewski)

This is the largest known 18-tuplet and the largest known case of 18
Simultaneous Primes.

Jarek
• ... Congratulations! http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated. -- Jens Kruse Andersen
Message 14 of 14 , Apr 26, 2010
Jarek wrote:
> 183837276562811649018077773 + d,
> d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70
> (27 digits, Apr 26, 2010, Jaroslaw Wroblewski)

Congratulations!
http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated.

--
Jens Kruse Andersen
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