20220828, 20:45  #23  
Einyen
Dec 2003
Denmark
3,413 Posts 
Quote:
I do not understand how you can make it so fast, there must be some modular trick I am missing. 

20220828, 21:09  #24  
Jan 2007
Germany
3·11·17 Posts 
Quote:
It is the 1st time I offer my code, written in Freebasic for a single run. I'm shure, it is one of the fastest code. Last fiddled with by Cybertronic on 20220828 at 21:12 

20220829, 02:24  #25 
"Matthew Anderson"
Dec 2010
Oregon, USA
2×19×31 Posts 
Admissable prime ktuple checker
Hi all,
I found a webpage that seems to be germane to this discussion. Chris Caldwell has his 'prime pages' with University of Tennessee at Martin. see this link. https://primes.utm.edu/glossary/includes/ktuple.php Maybee someone (like me) will find some almost prime constellations an put them on a webpage. By almost prime constellation, I mean not as dense as possible, but a similar pattern. Have a nice day. Matt 
20220829, 07:57  #26 
Jan 2007
Germany
561_{10} Posts 
status
Searching up to 32589158477190044730000 is done, no 19tuplet found.
Best was one hit with 13 conditions in order for 3718239377799223934593. These numbers have 16/19 are prime. 415755805068375308473 14968783430135985396883 28120524069667173601393 Code:
28120524069667173601393+00 is 3PRP! (0.000000 seconds) 28120524069667173601393+04 is 3PRP! (0.000000 seconds) 28120524069667173601393+06 is 3PRP! (0.000000 seconds) 28120524069667173601393+10 is 3PRP! (0.000000 seconds) 28120524069667173601393+16 is 3PRP! (0.000000 seconds) 28120524069667173601393+18 is 3PRP! (0.000000 seconds) 28120524069667173601393+24 is 3PRP! (0.000000 seconds) 28120524069667173601393+28 is 3PRP! (0.000000 seconds) 28120524069667173601393+30 is 3PRP! (0.000000 seconds) 28120524069667173601393+34 is 3PRP! (0.000000 seconds) 28120524069667173601393+40 is 3PRP! (0.000000 seconds) 28120524069667173601393+46 is 3PRP! (0.000000 seconds) 28120524069667173601393+48 is composite: [3C8425ABFBEF829E] (0.000000 seconds) 28120524069667173601393+54 is 3PRP! (0.000000 seconds) 28120524069667173601393+58 is composite: [1608EA1FFE278867] (0.000000 seconds) 28120524069667173601393+60 is composite: [246C14CD39E07B1F] (0.000000 seconds) 28120524069667173601393+66 is 3PRP! (0.000000 seconds) 28120524069667173601393+70 is 3PRP! (0.000000 seconds) 28120524069667173601393+76 is 3PRP! (0.000000 seconds) Estimate for 1st 19tuplet is round: (3,25^13)/1800 = 2400 cycles. 1 cycle = 4h on 32 threads. 2400 cycles is number 7.8e25 and it is a good deal for the smallest nontrivial 19tuplet ! With finetuning maybe under a year for me.....but not yet. Last fiddled with by Cybertronic on 20220829 at 08:04 
20220829, 11:22  #27 
Jan 2007
Germany
561_{10} Posts 
deep checking
brought me 17/19 are true
Code:
3525391639439773250083+00 is 3PRP! (0.000000 seconds) 3525391639439773250083+04 is 3PRP! (0.000000 seconds) 3525391639439773250083+06 is 3PRP! (0.000000 seconds) 3525391639439773250083+10 is 3PRP! (0.000000 seconds) 3525391639439773250083+16 is 3PRP! (0.000000 seconds) 3525391639439773250083+18 is 3PRP! (0.000000 seconds) 3525391639439773250083+24 is 3PRP! (0.000000 seconds) 3525391639439773250083+28 is 3PRP! (0.000000 seconds) 3525391639439773250083+30 is 3PRP! (0.000000 seconds) 3525391639439773250083+34 is 41813 · 175727 · 479797020767 3525391639439773250083+40 is 25693 · 137212144920397511 3525391639439773250083+46 is 3PRP! (0.000000 seconds) 3525391639439773250083+48 is 3PRP! (0.000000 seconds) 3525391639439773250083+54 is 3PRP! (0.000000 seconds) 3525391639439773250083+58 is 3PRP! (0.000000 seconds) 3525391639439773250083+60 is 3PRP! (0.000000 seconds) 3525391639439773250083+66 is 3PRP! (0.000000 seconds) 3525391639439773250083+70 is 3PRP! (0.000000 seconds) 3525391639439773250083+76 is 3PRP! (0.000000 seconds) 11490035915853116358673+00 is 3PRP! (0.000000 seconds) 11490035915853116358673+04 is 3PRP! (0.000000 seconds) 11490035915853116358673+06 is 3PRP! (0.000000 seconds) 11490035915853116358673+10 is 3PRP! (0.000000 seconds) 11490035915853116358673+16 is 3PRP! (0.000000 seconds) 11490035915853116358673+18 is 3PRP! (0.000000 seconds) 11490035915853116358673+24 is 3PRP! (0.000000 seconds) 11490035915853116358673+28 is 3PRP! (0.000000 seconds) 11490035915853116358673+30 is 3PRP! (0.000000 seconds) 11490035915853116358673+34 is 3PRP! (0.000000 seconds) 11490035915853116358673+40 is 2190756551 · 5244779896063 11490035915853116358673+46 is 3PRP! (0.000000 seconds) 11490035915853116358673+48 is 391847 · 9577441 · 3061648823 11490035915853116358673+54 is 3PRP! (0.000000 seconds) 11490035915853116358673+58 is 3PRP! (0.000000 seconds) 11490035915853116358673+60 is 3PRP! (0.000000 seconds) 11490035915853116358673+66 is 3PRP! (0.000000 seconds) 11490035915853116358673+70 is 3PRP! (0.000000 seconds) 11490035915853116358673+76 is 3PRP! (0.000000 seconds) Collect now numbers with 5 conditions...maybe there is to the end 18/19 ??? Last fiddled with by Cybertronic on 20220829 at 11:55 
20220829, 16:43  #28 
Jan 2007
Germany
3×11×17 Posts 
Searching up to 65'178'316'954'380'089'460'000 is done.
No 19tuplet with pattern d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70, 76 available. numbers with 16/19 conditions are: 61168575916820634489163 51376068524333215109383 48190289820404657882893 41319342180915627785893 2nd number with first 13 cond. are prime: 57188204801013850971343 Conclution: 1000 modern CPU cores can found this 19tuplet in 1 or 2 weeks. Last fiddled with by Cybertronic on 20220829 at 17:01 
20220829, 21:46  #29 
Jan 2007
Germany
231_{16} Posts 
There is an open question.
The unknown smallest nontrivial prime 19tuplet have a valid 18tuplet. I found in the archive: 183837276562811649018077773 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (27 digits, Apr 2010, Jaroslaw Wroblewski) 51342365971531191697537333 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26 digits, Mar 2009, Jaroslaw Wroblewski) 44453357465442632103684223 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26 digits, Feb 2009, Jaroslaw Wroblewski) 23531820918273007548405133 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26 digits, Jan 2009, Jaroslaw Wroblewski) 11298510058634407483251313 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (26 digits, Dec 2008, Jaroslaw Wroblewski) 1906230835046648293290043 + d, d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48, 54, 58, 60, 66, 70 (25 digits, 31 Jan 2001, Jörg Waldvogel & Peter Leikauf) / first nontrivial known to given pattern The first starting point is : 1906230835046648293290043 Question: Was found the other 18tuplets in logical order or not ?! Last fiddled with by Cybertronic on 20220829 at 21:46 
20220830, 09:45  #30 
Jan 2007
Germany
561_{10} Posts 
Got the answer.
1906230835046648293290043 is the new starting point and the other known 18tuplets was byproducts. 
20220907, 05:58  #31 
Jan 2007
Germany
3×11×17 Posts 
CRGreathouse look for the special prime 19tuplet X+d,d=0,8,24,48,80,120,168,224,288,360,440,528,624,728,840,960,1088,1224,1368
For number X=653, we get 18/19 are prime. Best runs up to 2'230'928'700'000'000 are 14/19 X=42584685212933 X=1599836864063783 There are round 142000 possible offset for 23# Last fiddled with by Cybertronic on 20220907 at 06:03 
20220907, 17:53  #32 
Aug 2006
5,987 Posts 

20220907, 18:27  #33 
Jan 2007
Germany
1061_{8} Posts 
Big Int
Download and rename into *.bi I have optimized now the special sieve incl deep sieving. Near 64'696'932'300'000'000 (6.4e16) now. 32 threads can scan 6.7e17 per day. Ratio for 5e16 ~ 1 : 2,4 [condition to condition] I believe, 2 weeks you must invest .... ~ 1e19 for the 1st hit, deal ? You can get the singlecore version with individual sieveranges. Last fiddled with by Cybertronic on 20220907 at 18:34 
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