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 Cybertronic 2021-10-13 20:29

[QUOTE=MattcAnderson;590487]Hi all,

Norman is doing a great project!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Matt[/QUOTE]

:bow:

At the moment , I calculate PI_14(10^22)

It tooks only 4 days per pattern plus any breaks.
Norman

P.S. Using PCs [2 Ryzen 7 1700 3 GHz]

 Cybertronic 2021-10-21 08:21

PI_14(10^22)

PI_14(10^22) is done.
There are 1810 14-tuplets up to 10^22
[URL]http://www.pzktupel.de/Tables.html[/URL]

next: PI_15(10^22)

 Cybertronic 2021-10-21 12:26

x congruent 29#

I updated the pattern list for prime 25..30 tuplets.
Prime 30-tuplets are the first case of x congruent 29#

[URL]http://www.pzktupel.de/ktpatt.html[/URL]

This is only a theoretical fact.

pattern : 0 4 6 10 16 18 28 30 34 36 48 58 60 64 66 70 76 78 84 88 94 100 106 108 114 118 120 126 130 136;

first number : 36990193 (modulo 223092870)

pattern : 0 6 10 16 18 22 28 30 36 42 48 52 58 60 66 70 72 76 78 88 100 102 106 108 118 120 126 130 132 136;

first number : 186102541 (modulo 223092870)

 mart_r 2021-10-21 18:14

Fabelhaft! :bow:

[QUOTE=Cybertronic;591212]
[URL]http://www.pzktupel.de/ktpatt.html[/URL]
[/QUOTE]

Call me naive, but I believe the first numbers of 6-tuplets can be restricted to 97 mod 210... have only looked at the first few examples though.

 sweety439 2021-10-21 18:33

[QUOTE=Cybertronic;591197]PI_14(10^22) is done.
There are 1810 14-tuplets up to 10^22
[URL]http://www.pzktupel.de/Tables.html[/URL]

next: PI_15(10^22)[/QUOTE]

I saw your page and I have a question: How many classes of prime n-tuplets?

[CODE]
n classes
1 {0} (1 class)
2 {0,2} (1 class)
3 {0,2,6}, {0,4,6} (2 classes)
4 {0,2,6,8} (1 class)
5 {0,2,6,8,12}, {0,4,6,10,12} (2 classes)
6 {0,4,6,10,12,16} (1 class)
7 {0,2,6,8,12,18,20}, {0,2,8,12,14,18,20} (2 classes)
8 {0,2,6,8,12,18,20,26}, {0,6,8,14,18,20,24,26}, {0,2,6,12,14,20,24,26} (3 classes)
9 {0,2,6,8,12,18,20,26,30}, {0,4,6,10,16,18,24,28,30}, {0,2,6,12,14,20,24,26,30}, {0,4,10,12,18,22,24,28,30} (4 classes)
10 {0,2,6,8,12,18,20,26,30,32}, {0,2,6,12,14,20,24,26,30,32} (2 classes)
[/CODE]

and I searched "[URL="https://oeis.org/search?q=1%2C+1%2C+2%2C+1%2C+2%2C+1%2C+2%2C+3%2C+4%2C+2&language=english&go=Search"]1, 1, 2, 1, 2, 1, 2, 3, 4, 2[/URL]" in OEIS, and no result about prime k-tuple found.

 Cybertronic 2021-10-21 18:43

Thanks Martin, this was not optimal. Overlooked !:smile:

[QUOTE=mart_r;591254]Fabelhaft! :bow:

Call me naive, but I believe the first numbers of 6-tuplets can be restricted to 97 mod 210... have only looked at the first few examples though.[/QUOTE]

 mart_r 2021-10-21 18:46

[QUOTE=sweety439;591255]I saw your page and I have a question: How many classes of prime n-tuplets?

[CODE]
n classes
1 {0} (1 class)
2 {0,2} (1 class)
3 {0,2,6}, {0,4,6} (2 classes)
4 {0,2,6,8} (1 class)
5 {0,2,6,8,12}, {0,4,6,10,12} (2 classes)
6 {0,4,6,10,12,16} (1 class)
7 {0,2,6,8,12,18,20}, {0,2,8,12,14,18,20} (2 classes)
8 {0,2,6,8,12,18,20,26}, {0,6,8,14,18,20,24,26}, {0,2,6,12,14,20,24,26} (3 classes)
9 {0,2,6,8,12,18,20,26,30}, {0,4,6,10,16,18,24,28,30}, {0,2,6,12,14,20,24,26,30}, {0,4,10,12,18,22,24,28,30} (4 classes)
10 {0,2,6,8,12,18,20,26,30,32}, {0,2,6,12,14,20,24,26,30,32} (2 classes)
[/CODE]

and I searched "[URL="https://oeis.org/search?q=1%2C+1%2C+2%2C+1%2C+2%2C+1%2C+2%2C+3%2C+4%2C+2&language=english&go=Search"]1, 1, 2, 1, 2, 1, 2, 3, 4, 2[/URL]" in OEIS, and no result about prime k-tuple found.[/QUOTE]

Try one term less in the search and you'll find A[OEIS]083409[/OEIS].

 Cybertronic 2021-10-21 18:53

Helle sweety439 !

> I saw your page and I have a question: How many classes of prime n-tuplets?

The exact class for a prime n-tuplet I had take over from Tony Forbes.

What you mean ?

Here is another list:

[url]http://www.opertech.com/primes/k-tuples.html[/url]

 Cybertronic 2021-10-22 06:21

correction #36. It is 23#, not 29#

:rolleyes:

[Prime 30-tuplets are the first case of x congruent 23#]

And so on...

 Cybertronic 2021-10-22 12:06

up to prime 50-tuplet

The congruent-calculation for all patterns up to prime 50-tuplet is done.

See: [url]http://www.pzktupel.de/ktpatt.html[/url]

The largest modulo-number is (modulo 10555815270)

I hope it is correct.

 Cybertronic 2021-10-24 12:57

new color scheme

[url]http://www.pzktupel.de/ktuplets[/url]

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