smallest n-digit prime k-tuplet

Cybertronic · 2020-12-19, 16:09

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.

mart_r · 2020-12-21, 18:39

Eine exzellente Zusammenstellung - Respekt vor der Arbeit, die dahintersteckt

Cybertronic · 2020-12-21, 21:41

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

Cybertronic · 2020-12-28, 10:13

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

Cybertronic · 2020-12-31, 17:38

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

Cybertronic · 2021-01-20, 10:38

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

Cybertronic · 2021-01-24, 06:41

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

Cybertronic · 2021-01-25, 08:15

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...

kruoli · 2021-01-25, 13:22

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

factordb.com says it is only prime for d=0.

axn · 2021-01-25, 15:24

The given value looks like the end point.

The actual starting point is 10000000000001275924044876917671361

Cybertronic · 2021-01-25, 17:32

Quote:

Originally Posted by axn

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

2020-12-21, 18:39	#2
mart_r Dec 2008 you know...around... 1010010111₂ Posts	Eine exzellente Zusammenstellung - Respekt vor der Arbeit, die dahintersteckt Last fiddled with by mart_r on 2020-12-21 at 18:41

2020-12-21, 21:41	#3
Cybertronic Jan 2007 Germany 328₁₀ Posts	Oh ,vielen Dank für das dicke Lob ! 😃 ( Thank you ) Last fiddled with by Cybertronic on 2020-12-21 at 21:53

2021-01-25, 08:15	#8
Cybertronic Jan 2007 Germany 2³×41 Posts	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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2020-12-28, 10:13	#4
Cybertronic Jan 2007 Germany 2³×41 Posts	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

2021-01-24, 06:41	#7
Cybertronic Jan 2007 Germany 2³×41 Posts	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

2021-01-25, 13:22	#9
kruoli "Oliver" Sep 2017 Porta Westfalica, DE 21B₁₆ Posts	There seems to be something wrong with the 14-tuplet. factordb.com says it is only prime for d=0.

2021-01-25, 15:24	#10
axn Jun 2003 5,051 Posts	The given value looks like the end point. The actual starting point is 10000000000001275924044876917671361