smallest n-digit prime k-tuplet
 

Hello,

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


The mainthread is in german. [url]https://matheplanet.de/matheplanet/nuke/html/viewtopic.php?topic=232720&start=0[/url]


Latest entry: smallest 200-digit prime octuplet.



Status: 19.12.2020


I try to keep actual...maybe it is interesting for you.

Eine exzellente Zusammenstellung - Respekt vor der Arbeit, die dahintersteckt :tu:

Oh ,vielen Dank für das dicke Lob ! 😃 ( Thank you )

[SIZE=2]Update: smallest 200 digit prime octuplet found to pattern d=0,6,8,14,18,20,24,26

[FONT=Arial]1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000000000000004456720213751803153+d, d=0,6,8,14,18,20,24,26[/FONT][/SIZE]

[SIZE=2]Update: smallest 200 digit prime octuplet found to pattern d=0,2,6,12,14,20,24,26

[FONT=Arial]1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000000000000000589262946758538727+d, d=0,2,6,12,14,20,24,26[/FONT][/SIZE]

Update:

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


[SIZE=2]10^149+177107310312127411+d,d=0,2,6, 8,12,18,20,26
[/SIZE]
[SIZE=2]10^149+883945334707753267+d,d=0,2,6,12,14,20,24,26
[/SIZE]
[SIZE=2]10^149+935628779313782743+d,d=0,6,8,14,18,20,24,26[/SIZE]
[SIZE=2]

[/SIZE]

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

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...

There seems to be something wrong with the 14-tuplet. :unsure:

[URL="http://factordb.com/index.php?query=10000000000001275924044876917671411%2B2*x&use=x&x=0&VP=on&VC=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=24&format=1"]factordb.com[/URL] says it is only prime for d=0.

The given value looks like the end point.

The actual starting point is [URL="http://factordb.com/index.php?query=10000000000001275924044876917671361%2Bn&use=n&n=0&VP=on&VC=on&EV=on&PR=on&PRP=on&U=on&perpage=14&format=1&sent=Show"]10000000000001275924044876917671361[/URL]

[QUOTE=axn;570083]The given value looks like the end point.

The actual starting point is [URL="http://factordb.com/index.php?query=10000000000001275924044876917671361%2Bn&use=n&n=0&VP=on&VC=on&EV=on&PR=on&PRP=on&U=on&perpage=14&format=1&sent=Show"]10000000000001275924044876917671361[/URL][/QUOTE]


Oh yes axn, this is correct...my mistake :down:
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