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Old 2021-03-22, 08:06   #34
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Default Update PDF-File 22-03-2021

Update.
Attached Files
File Type: pdf smallest-n-digit-prime-k-tuplets_main-list.pdf (167.7 KB, 69 views)
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Old 2021-03-30, 19:38   #35
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Default complete set of smallest 30-digit prime 15-tuplets

100000001341915517111319670637+d,d=00,02,06,12,14,20,24,26,30,36,42,44,50,54,56
100000001651438068367136632687+d,d=00,02,06,12,14,20,26,30,32,36,42,44,50,54,56
100000008317726120972779285703+d,d=00,06,08,14,20,24,26,30,36,38,44,48,50,54,56
100000005745569203832854981801+d,d=00,02,06,08,12,18,20,26,30,32,36,42,48,50,56 (99,99% sure)

next is: Try to find the smallest set of 25-digit prime 17-tuplet....and !

I found after few hours the 1st possible combination
1024494443639408527082233+d,d=00,04,06,10,16,18,24,28,30,34,40,46,48,54,58,60,66


This is my first prime 17-tuplet !

Last fiddled with by Cybertronic on 2021-03-30 at 19:40
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Old 2021-04-13, 13:28   #36
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Default second 25-digit prime 17-tuplet

The 2nd smallest 25-digit prime 17-tuplet is known.

1234254817970443433617451+d,d=00,06,08,12,18,20,26,32,36,38,42,48,50,56,60,62,66

Last fiddled with by Cybertronic on 2021-04-13 at 13:28
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Old 2021-04-28, 11:10   #37
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Default 3rd kind of smallest 25-digit prime 17-tuplet

...is known

1271960773255490350812797+d,d=0,2,6,12,14,20,24,26,30,36,42,44,50,54,56,62,66

[comuting time 2 weeks]

BTW, for pattern d=0,4,10,12,16,22,24,30,36,40,42,46,52,54,60,64,66

is the smallest number (see OEIS) N=734975534793324512717947. I think this is very large so I make a double test up to 1e23.
Maybe there are a smaller one.

Last fiddled with by Cybertronic on 2021-04-28 at 11:16
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Old 2021-05-22, 14:42   #38
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Default 2000 / 3000 digit smallest proven! prime k-tuplets

reference: factordb.com

2000-digits

k: number to pattern d
1: 10^1999+7321 / proven prime
2: 10^1999+89316289+d, d=0,2 / proven primes
3: 10^1999+27107552191+d, d=0,2,6 / proven primes
3: 10^1999+38866053453+d, d=0,4,6 / proven primes
4: 10^1999+205076414983951+d d=0,2,6,8 / found by Gerd Lamprecht (2017) & proven primes

3000-digits

k: number to pattern d
1: 10^2999+1887 / proven prime
2: 10^2999+18893101+d, d=0,2 / proven primes
3: 10^2999+25740029131+d, d=0,2,6 / proven primes
3: 10^2999+37274603937+d, d=0,4,6 / proven primes

Last fiddled with by Cybertronic on 2021-05-22 at 14:43
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Old 2021-05-23, 04:19   #39
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Default 4000 digit - smallest proven! prime k-tuplets

reference: factordb.com

4000-digits

k: number to pattern d
1: 10^3999+4771 / proven prime by Giovanni and Marco La Barbera (2001)
2: 10^3999+153668401+d, d=0,2 / proven primes
3: 10^3999+182402621497+d, d=0,2,6 / proven primes
3: 10^3999+243095638113+d, d=0,4,6 / proven primes
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Old 2021-05-23, 15:23   #40
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Default 5000 digit - smallest twins

5000 digits : 10^4999+45171901+d, d=0,2 /now proven primes
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Old 2021-06-01, 05:54   #41
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Default new proven primes,twins,triplets

smallest x1000-digit prime

6000 digits :10^5999+29379
7000 digits :10^6999+33187
8000 digits :10^7999+35887 / proven primes by Robert Gelhar (05/2021,Primo)
9000 digits :10^8999+3541 / proven primes by Robert Gelhar (05/2021,Primo)

smallest x1000-digit twin prime

7000 digits : 10^6999+151203769+d,d=0,2 / proven primes by Robert Gelhar (05/2021,Primo)
8000 digits :10^7999+439617139+d,d=0,2 / proven primes by Robert Gelhar (05/2021,Primo)
9000 digit :10^8999+1321587+d,d=0,2 / proven primes by Robert Gelhar (05/2021,Primo)

smallest 5000-digit prime triplets


10^4999+70852892827+d d=0,2,6 / proven primes by Norman Luhn (Primo)
10^4999+244793127627+d d=0,4,6 / proven primes by Norman Luhn (Primo)
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Old 2021-06-03, 20:26   #42
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Default smallets gigantic twin

10^9999+2421018649+d,d=0,2 is the smallest gigantic twin.

Found by Dirk Augustin in 2010 and now proven primes by Norman Luhn.
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Old 2021-06-05, 12:52   #43
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Default smallest 20000-digit twins

I found the smallest 20000 digit twin PRPs.
10^19999+1514722609+d,d=0,2
______

Norman
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Old 2021-06-08, 03:52   #44
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Default 4th kind of smallest 25-digit prime 17-tuplet found

The 4th kind ist found, so the complete set of smallest 25 digit prime 17-tuplet is known.


1024494443639408527082233+d,d=00,04,06,10,16,18,24,28,30,34,40,46,48,54,58,60,66
1234254817970443433617451+d,d=00,06,08,12,18,20,26,32,36,38,42,48,50,56,60,62,66
1271960773255490350812797+d,d=00,02,06,12,14,20,24,26,30,36,42,44,50,54,56,62,66
1341829940444122313597407+d,d=00,04,10,12,16,22,24,30,36,40,42,46,52,54,60,64,66


latest update:
Attached Files
File Type: pdf smallest-n-digit-prime-k-tuplets_main-list.pdf (189.7 KB, 35 views)
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