smallest n-digit prime k-tuplet - Page 2

Cybertronic · 2021-01-31, 08:17

Update:

The 2nd "smallest 35-digit prime 14-tuplet is also known.
10000000000009283441665311798539399+d,d=0,2,8,14,18,20,24,30,32,38,42,44,48,50

Cybertronic · 2021-02-04, 21:16

Update
// Both kinds of "smallest 25-digit prime 16-tuplet" are known //

1015074281315414986743013+d,d=0,4,6,10,16,18,24,28,30,34,40,46,48,54,58,60
1008037335701436528651167+d,d=0,2,6,12,14,20,26,30,32,36,42,44,50,54,56,60

computing time: 105h

Hardware: 2 Ryzen 7 1700 @ 3GHz

Cybertronic · 2021-02-07, 20:34

Update
// Both kinds of "smallest 45-digit prime 12-tuplet" are known //
100000000000000000000000172106518341892028911+d,d=0,2,6,8,12,18,20,26,30,32,36,42
100000000000000000000000142880384538471179727+d,d=0,6,10,12,16,22,24,30,34,36,40,42

Cybertronic · 2021-02-08, 15:09

45-digit prime 12-tuplet - maybe incorrect and double check now.

Cybertronic · 2021-02-10, 04:30

// Both kinds of "smallest 45-digit prime 12-tuplet" are known //
H/L: Offsetabschätzung nach Hardy-Littlewood für Primzahl 12-Tupel
100000000000000000000000172106518341892028911+d,d=0,2,6,8,12,18,20,26,30,32,36,42 ; H/L: 1e20
100000000000000000000000041408120385362420817+d,d=0,6,10,12,16,22,24,30,34,36,40,42 ; H/L: 1e20

Cybertronic · 2021-02-16, 10:21

Smallest 50-digit prime 12-tuplet to pattern d=0,2,6,8,12,18,20,26,30,32,36,42 is now known.

10000000000000000000000000000896396147387349765031+d

Time to compute: ~7d

Cybertronic · 2021-02-24, 05:15

Searching for the set of "smallest 50-digit prime 12-tuplet" is done.

Here an overview of smallest 50-digit prime k-tuplet. [k=1 to 12].

k: number to pattern d
01: 10000000000000000000000000000000000000000000000009
02: 10000000000000000000000000000000000000000000008281+d d=0,2
03: 10000000000000000000000000000000000000000000136807+d d=0,2,6
03: 10000000000000000000000000000000000000000001447533+d d=0,4,6
04: 10000000000000000000000000000000000000000058537891+d d=0,2,6,8 / found by G. John Stevens (1995)
05: 10000000000000000000000000000000000000002625950761+d d=0,2,6,8,12
05: 10000000000000000000000000000000000000000108888657+d d=0,4,6,10,12
06: 10000000000000000000000000000000000000012427403607+d d=0,4,6,10,12,16
07: 10000000000000000000000000000000000001920433761121+d d=0,2,6,8,12,18,20
07: 10000000000000000000000000000000000005649726612769+d d=0,2,8,12,14,18,20
08: 10000000000000000000000000000000000079626461485831+d d=0,2,6,8,12,18,20,26
08: 10000000000000000000000000000000000119829260675203+d d=0,6,8,14,18,20,24,26
08: 10000000000000000000000000000000000030593919062857+d d=0,2,6,12,14,20,24,26
09: 10000000000000000000000000000000000500925570224521+d d=0,2,6,8,12,18,20,26,30
09: 10000000000000000000000000000000005212838536064887+d d=0,2,6,12,14,20,24,26,30
09: 10000000000000000000000000000000003526198250883003+d d=0,4,6,10,16,18,24,28,30
09: 10000000000000000000000000000000001731699431041809+d d=0,4,10,12,18,22,24,28,30
10: 10000000000000000000000000000000005620800916143211+d d=0,2,6,8,12,18,20,26,30,32
10: 10000000000000000000000000000000921015585010336777+d d=0,2,6,12,14,20,24,26,30,32
11: 10000000000000000000000000000021389429204344782841+d d=0,2,6,8,12,18,20,26,30,32,36
11: 10000000000000000000000000000012954750883079039103+d d=0,4,6,10,16,18,24,28,30,34,36
12: 10000000000000000000000000000896396147387349765031+d d=0,2,6,8,12,18,20,26,30,32,36,42
12: 10000000000000000000000000000929532973818094710897+d d=0,6,10,12,16,22,24,30,34,36,40,42

LaurV · 2021-02-24, 06:52

Nice!
Congrats!

(ignorant) Question: Are those all possible/minimal constellations? If not, which constellation is missing?

Cybertronic · 2021-02-24, 07:05

Quote:

Originally Posted by LaurV

Nice!
Congrats!

(ignorant) Question: Are those all possible/minimal constellations? If not, which constellation is missing?

These are all minimal constellations. Searching was systematic.

Update PDF-Document / 24th Feb. 2021

Cybertronic · 2021-02-24, 16:10

Next: smallest 40-digit prime 13-tuplet

preview, 1st (possible) kind is found:

1000000000000000000282197071067938130221+d,d=0,2,6,8,12,18,20,26,30,32,36,42,48

Cybertronic · 2021-03-03, 12:14

2nd smallest 40-digit prime 13-tuplet is found.

1000000000000000002713562652524314606953+d,d=00,04,06,10,16,18,24,28,30,34,40,46,48

BTW, during the searching , I can confirm that the Hardy-Littlewood estimating is correct.

2021-01-31, 08:17	#12
Cybertronic Jan 2007 Germany 300₁₀ Posts	Update: The 2nd "smallest 35-digit prime 14-tuplet is also known. 10000000000009283441665311798539399+d,d=0,2,8,14,18,20,24,30,32,38,42,44,48,50 Last fiddled with by Cybertronic on 2021-01-31 at 08:18

2021-02-04, 21:16	#13
Cybertronic Jan 2007 Germany 300₁₀ Posts	Update // Both kinds of "smallest 25-digit prime 16-tuplet" are known // 1015074281315414986743013+d,d=0,4,6,10,16,18,24,28,30,34,40,46,48,54,58,60 1008037335701436528651167+d,d=0,2,6,12,14,20,26,30,32,36,42,44,50,54,56,60 computing time: 105h Hardware: 2 Ryzen 7 1700 @ 3GHz Last fiddled with by Cybertronic on 2021-02-04 at 21:18

2021-02-16, 10:21	#17
Cybertronic Jan 2007 Germany 2²·3·5² Posts	Smallest 50-digit prime 12-tuplet to pattern d=0,2,6,8,12,18,20,26,30,32,36,42 is now known. 10000000000000000000000000000896396147387349765031+d Time to compute: ~7d Last fiddled with by Cybertronic on 2021-02-16 at 10:55

2021-02-24, 05:15	#18
Cybertronic Jan 2007 Germany 2²×3×5² Posts	Searching for the set of "smallest 50-digit prime 12-tuplet" is done. Here an overview of smallest 50-digit prime k-tuplet. [k=1 to 12]. k: number to pattern d 01: 10000000000000000000000000000000000000000000000009 02: 10000000000000000000000000000000000000000000008281+d d=0,2 03: 10000000000000000000000000000000000000000000136807+d d=0,2,6 03: 10000000000000000000000000000000000000000001447533+d d=0,4,6 04: 10000000000000000000000000000000000000000058537891+d d=0,2,6,8 / found by G. John Stevens (1995) 05: 10000000000000000000000000000000000000002625950761+d d=0,2,6,8,12 05: 10000000000000000000000000000000000000000108888657+d d=0,4,6,10,12 06: 10000000000000000000000000000000000000012427403607+d d=0,4,6,10,12,16 07: 10000000000000000000000000000000000001920433761121+d d=0,2,6,8,12,18,20 07: 10000000000000000000000000000000000005649726612769+d d=0,2,8,12,14,18,20 08: 10000000000000000000000000000000000079626461485831+d d=0,2,6,8,12,18,20,26 08: 10000000000000000000000000000000000119829260675203+d d=0,6,8,14,18,20,24,26 08: 10000000000000000000000000000000000030593919062857+d d=0,2,6,12,14,20,24,26 09: 10000000000000000000000000000000000500925570224521+d d=0,2,6,8,12,18,20,26,30 09: 10000000000000000000000000000000005212838536064887+d d=0,2,6,12,14,20,24,26,30 09: 10000000000000000000000000000000003526198250883003+d d=0,4,6,10,16,18,24,28,30 09: 10000000000000000000000000000000001731699431041809+d d=0,4,10,12,18,22,24,28,30 10: 10000000000000000000000000000000005620800916143211+d d=0,2,6,8,12,18,20,26,30,32 10: 10000000000000000000000000000000921015585010336777+d d=0,2,6,12,14,20,24,26,30,32 11: 10000000000000000000000000000021389429204344782841+d d=0,2,6,8,12,18,20,26,30,32,36 11: 10000000000000000000000000000012954750883079039103+d d=0,4,6,10,16,18,24,28,30,34,36 12: 10000000000000000000000000000896396147387349765031+d d=0,2,6,8,12,18,20,26,30,32,36,42 12: 10000000000000000000000000000929532973818094710897+d d=0,6,10,12,16,22,24,30,34,36,40,42 Last fiddled with by Cybertronic on 2021-02-24 at 05:18

2021-02-24, 06:52	#19
LaurV Romulan Interpreter Jun 2011 Thailand 9377₁₀ Posts	Nice! Congrats! (ignorant) Question: Are those all possible/minimal constellations? If not, which constellation is missing? Last fiddled with by LaurV on 2021-02-24 at 06:52

2021-02-08, 15:09	#15
Cybertronic Jan 2007 Germany 2²×3×5² Posts	45-digit prime 12-tuplet - maybe incorrect and double check now.

2021-02-10, 04:30	#16
Cybertronic Jan 2007 Germany 2²×3×5² Posts	// Both kinds of "smallest 45-digit prime 12-tuplet" are known // H/L: Offsetabschätzung nach Hardy-Littlewood für Primzahl 12-Tupel 100000000000000000000000172106518341892028911+d,d=0,2,6,8,12,18,20,26,30,32,36,42 ; H/L: 1e20 100000000000000000000000041408120385362420817+d,d=0,6,10,12,16,22,24,30,34,36,40,42 ; H/L: 1e20

2021-02-24, 16:10	#21
Cybertronic Jan 2007 Germany 300₁₀ Posts	Next: smallest 40-digit prime 13-tuplet preview, 1st (possible) kind is found: 1000000000000000000282197071067938130221+d,d=0,2,6,8,12,18,20,26,30,32,36,42,48

2021-03-03, 12:14	#22
Cybertronic Jan 2007 Germany 12C₁₆ Posts	2nd smallest 40-digit prime 13-tuplet is found. 1000000000000000002713562652524314606953+d,d=00,04,06,10,16,18,24,28,30,34,40,46,48 BTW, during the searching , I can confirm that the Hardy-Littlewood estimating is correct.

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