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Old 2021-10-13, 20:29   #34
Cybertronic
 
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Quote:
Originally Posted by MattcAnderson View Post
Hi all,

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

Matt




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]

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Old 2021-10-21, 08:21   #35
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Default PI_14(10^22)

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


next: PI_15(10^22)

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Old 2021-10-21, 12:26   #36
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Default x congruent 29#

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



http://www.pzktupel.de/ktpatt.html


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)

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Old 2021-10-21, 18:14   #37
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Fabelhaft!

Quote:
Originally Posted by Cybertronic View Post
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.
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Old 2021-10-21, 18:33   #38
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Quote:
Originally Posted by Cybertronic View Post
PI_14(10^22) is done.
There are 1810 14-tuplets up to 10^22
http://www.pzktupel.de/Tables.html


next: PI_15(10^22)
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)
and I searched "1, 1, 2, 1, 2, 1, 2, 3, 4, 2" in OEIS, and no result about prime k-tuple found.
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Old 2021-10-21, 18:43   #39
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Thanks Martin, this was not optimal. Overlooked !



Quote:
Originally Posted by mart_r View Post
Fabelhaft!



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.
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Old 2021-10-21, 18:46   #40
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Quote:
Originally Posted by sweety439 View Post
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)
and I searched "1, 1, 2, 1, 2, 1, 2, 3, 4, 2" in OEIS, and no result about prime k-tuple found.
Try one term less in the search and you'll find A083409.
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Old 2021-10-21, 18:53   #41
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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:


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


Helpfully?
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Old 2021-10-22, 06:21   #42
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Default correction #36. It is 23#, not 29#




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



And so on...

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Old 2021-10-22, 12:06   #43
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Default up to prime 50-tuplet

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



See: http://www.pzktupel.de/ktpatt.html


The largest modulo-number is (modulo 10555815270)


I hope it is correct.

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Old 2021-10-24, 12:57   #44
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Default new color scheme

http://www.pzktupel.de/ktuplets
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