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Old 2020-12-19, 16:09   #1
Cybertronic
 
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Default smallest n-digit prime k-tuplet

Hello,

I will try to supply here my smallest prime k-tuplet project.


The mainthread is in german. https://matheplanet.de/matheplanet/n...232720&start=0


Latest entry: smallest 200-digit prime octuplet.



Status: 19.12.2020


I try to keep actual...maybe it is interesting for you.
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File Type: pdf smallest-x5_x100-digit-prime-k-tuplets.pdf (149.4 KB, 59 views)
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Old 2020-12-21, 18:39   #2
mart_r
 
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you know...around...

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Eine exzellente Zusammenstellung - Respekt vor der Arbeit, die dahintersteckt

Last fiddled with by mart_r on 2020-12-21 at 18:41
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Old 2020-12-21, 21:41   #3
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Oh ,vielen Dank für das dicke Lob ! 😃 ( Thank you )

Last fiddled with by Cybertronic on 2020-12-21 at 21:53
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Old 2020-12-28, 10:13   #4
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Update: smallest 200 digit prime octuplet found to pattern d=0,6,8,14,18,20,24,26

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000000000000004456720213751803153+d, d=0,6,8,14,18,20,24,26
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Old 2020-12-31, 17:38   #5
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Update: smallest 200 digit prime octuplet found to pattern d=0,2,6,12,14,20,24,26

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000000000000000589262946758538727+d, d=0,2,6,12,14,20,24,26
Attached Files
File Type: pdf smallest-x5_x100-digit-prime-k-tuplets.pdf (149.3 KB, 29 views)

Last fiddled with by Cybertronic on 2020-12-31 at 17:51
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Old 2021-01-20, 10:38   #6
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Update:

The 3 kinds of "Smallest 150-digit prime octuplets" are:


10^149+177107310312127411+d,d=0,2,6, 8,12,18,20,26

10^149+883945334707753267+d,d=0,2,6,12,14,20,24,26

10^149+935628779313782743+d,d=0,6,8,14,18,20,24,26


Attached Files
File Type: pdf smallest-n-digit-prime-k-tuplets_main-list.pdf (149.7 KB, 32 views)

Last fiddled with by Cybertronic on 2021-01-20 at 10:39
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Old 2021-01-24, 06:41   #7
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Update:
the smallest 35-digit prime 13-tuplets to each pattern are:


10000000000000324000701496110723931+d,d=00,06,12,16,18,22,28,30,36,40,42,46,48
10000000000000015141548551355951851+d,d=00,02,06,08,12,18,20,26,30,32,36,42,48
10000000000000094989640220894283993+d,d=00,04,06,10,16,18,24,28,30,34,40,46,48
10000000000000325778825790175217703+d,d=00,04,06,10,16,18,24,28,30,34,36,46,48
10000000000000108412629077454977119+d,d=00,02,08,14,18,20,24,30,32,38,42,44,48
10000000000000054122451329461300669+d,d=00,02,12,14,18,20,24,30,32,38,42,44,48
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Old 2021-01-25, 08:15   #8
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Update:


smallest 35-digit prime 14-tuplet found.

10000000000001275924044876917671411+d,d=0,2,6,8,12,18,20,26,30,32,36,42,48,50


Actual the 3rd largest known 14-tuplet.

computing time ~ 18h

The 2nd kind 14-tuplet is in process...

Last fiddled with by Cybertronic on 2021-01-25 at 08:15
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Old 2021-01-25, 13:22   #9
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There seems to be something wrong with the 14-tuplet.

factordb.com says it is only prime for d=0.
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Old 2021-01-25, 15:24   #10
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The given value looks like the end point.

The actual starting point is 10000000000001275924044876917671361
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Old 2021-01-25, 17:32   #11
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Quote:
Originally Posted by axn View Post
The given value looks like the end point.

The actual starting point is 10000000000001275924044876917671361

Oh yes axn, this is correct...my mistake
Thank you !


So, once more...

1st kind of smallest 35-digit prime 14-tuplet starts with
10000000000001275924044876917671361+d,d=0,2,6,8,12,18,20,26,30,32,36,42,48,50

Last fiddled with by Cybertronic on 2021-01-25 at 17:40
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