smallest n-digit prime k-tuplet - Page 4

Cybertronic · 2021-03-22, 08:06

Update.

Cybertronic · 2021-03-30, 19:38

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 !

Cybertronic · 2021-04-13, 13:28

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

Cybertronic · 2021-04-28, 11:10

...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.

Cybertronic · 2021-05-22, 14:42

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

Cybertronic · 2021-05-23, 04:19

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

Cybertronic · 2021-05-23, 15:23

5000 digits : 10^4999+45171901+d, d=0,2 /now proven primes

Cybertronic · 2021-06-01, 05:54

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)

Cybertronic · 2021-06-03, 20:26

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.

Cybertronic · 2021-06-05, 12:52

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

Norman

Cybertronic · 2021-06-08, 03:52

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:

2021-03-30, 19:38	#35
Cybertronic Jan 2007 Germany 2³·41 Posts	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

2021-04-13, 13:28	#36
Cybertronic Jan 2007 Germany 2³×41 Posts	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

2021-04-28, 11:10	#37
Cybertronic Jan 2007 Germany 2³×41 Posts	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

2021-05-22, 14:42	#38
Cybertronic Jan 2007 Germany 2³·41 Posts	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

2021-05-23, 04:19	#39
Cybertronic Jan 2007 Germany 2³×41 Posts	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

2021-05-23, 15:23	#40
Cybertronic Jan 2007 Germany 2³×41 Posts	5000 digit - smallest twins 5000 digits : 10^4999+45171901+d, d=0,2 /now proven primes

2021-06-01, 05:54	#41
Cybertronic Jan 2007 Germany 2³·41 Posts	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)

2021-06-03, 20:26	#42
Cybertronic Jan 2007 Germany 328₁₀ Posts	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.

2021-06-05, 12:52	#43
Cybertronic Jan 2007 Germany 148₁₆ Posts	smallest 20000-digit twins I found the smallest 20000 digit twin PRPs. 10^19999+1514722609+d,d=0,2 ______ Norman

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