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2021-10-13, 20:29   #34
Cybertronic

Jan 2007
Germany

421 Posts

Quote:
 Originally Posted by MattcAnderson 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]

Last fiddled with by Cybertronic on 2021-10-13 at 20:33

 2021-10-21, 08:21 #35 Cybertronic     Jan 2007 Germany 421 Posts 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) Last fiddled with by Cybertronic on 2021-10-21 at 08:22
 2021-10-21, 12:26 #36 Cybertronic     Jan 2007 Germany 421 Posts 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) Last fiddled with by Cybertronic on 2021-10-21 at 12:34
2021-10-21, 18:14   #37
mart_r

Dec 2008
you know...around...

10101011112 Posts

Fabelhaft!

Quote:
 Originally Posted by Cybertronic http://www.pzktupel.de/ktpatt.html
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.

2021-10-21, 18:33   #38
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

22×19×41 Posts

Quote:
 Originally Posted by Cybertronic 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.

2021-10-21, 18:43   #39
Cybertronic

Jan 2007
Germany

421 Posts

Thanks Martin, this was not optimal. Overlooked !

Quote:
 Originally Posted by mart_r 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.

2021-10-21, 18:46   #40
mart_r

Dec 2008
you know...around...

3·229 Posts

Quote:
 Originally Posted by sweety439 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.

 2021-10-21, 18:53 #41 Cybertronic     Jan 2007 Germany 421 Posts 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?
 2021-10-22, 06:21 #42 Cybertronic     Jan 2007 Germany 421 Posts correction #36. It is 23#, not 29# [Prime 30-tuplets are the first case of x congruent 23#] And so on... Last fiddled with by Cybertronic on 2021-10-22 at 06:22
 2021-10-22, 12:06 #43 Cybertronic     Jan 2007 Germany 421 Posts 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. Last fiddled with by Cybertronic on 2021-10-22 at 12:15
 2021-10-24, 12:57 #44 Cybertronic     Jan 2007 Germany 421 Posts new color scheme

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