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Old 2022-08-28, 20:45   #23
ATH
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Quote:
Originally Posted by Cybertronic View Post
I have run now 32 threads...will see, how many conditions in order are true ... up to 32589158477190044730000
Tooks me 4h, so the offset progress (averaged) is 7e16/s and core
Very nice!

I do not understand how you can make it so fast, there must be some modular trick I am missing.
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Old 2022-08-28, 21:09   #24
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Quote:
Originally Posted by ATH View Post
Very nice!

I do not understand how you can make it so fast, there must be some modular trick I am missing.

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.
Attached Files
File Type: txt 19TP2_53.txt (77.0 KB, 42 views)

Last fiddled with by Cybertronic on 2022-08-28 at 21:12
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Old 2022-08-29, 02:24   #25
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Smile Admissable prime k-tuple checker

Hi all,
I found a web-page 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 web-page.
By almost prime constellation, I mean not as dense as possible, but a similar pattern.

Have a nice day.

Matt
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Old 2022-08-29, 07:57   #26
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Searching up to 32589158477190044730000 is done, no 19-tuplet 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 3-PRP! (0.000000 seconds)
28120524069667173601393+04 is 3-PRP! (0.000000 seconds)
28120524069667173601393+06 is 3-PRP! (0.000000 seconds)
28120524069667173601393+10 is 3-PRP! (0.000000 seconds)
28120524069667173601393+16 is 3-PRP! (0.000000 seconds)
28120524069667173601393+18 is 3-PRP! (0.000000 seconds)
28120524069667173601393+24 is 3-PRP! (0.000000 seconds)
28120524069667173601393+28 is 3-PRP! (0.000000 seconds)
28120524069667173601393+30 is 3-PRP! (0.000000 seconds)
28120524069667173601393+34 is 3-PRP! (0.000000 seconds)
28120524069667173601393+40 is 3-PRP! (0.000000 seconds)
28120524069667173601393+46 is 3-PRP! (0.000000 seconds)
28120524069667173601393+48 is composite: [3C8425ABFBEF829E] (0.000000 seconds)
28120524069667173601393+54 is 3-PRP! (0.000000 seconds)
28120524069667173601393+58 is composite: [1608EA1FFE278867] (0.000000 seconds)
28120524069667173601393+60 is composite: [246C14CD39E07B1F] (0.000000 seconds)
28120524069667173601393+66 is 3-PRP! (0.000000 seconds)
28120524069667173601393+70 is 3-PRP! (0.000000 seconds)
28120524069667173601393+76 is 3-PRP! (0.000000 seconds)
Ratio: 1: 2,97 for 23 digits , should be the target have 27 digits, we have ratio ~ 1:3,5
Estimate for 1st 19-tuplet 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 19-tuplet !
With finetuning maybe under a year for me.....but not yet.

Last fiddled with by Cybertronic on 2022-08-29 at 08:04
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Old 2022-08-29, 11:22   #27
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Default deep checking

brought me 17/19 are true
Code:
3525391639439773250083+00 is 3-PRP! (0.000000 seconds)
3525391639439773250083+04 is 3-PRP! (0.000000 seconds)
3525391639439773250083+06 is 3-PRP! (0.000000 seconds)
3525391639439773250083+10 is 3-PRP! (0.000000 seconds)
3525391639439773250083+16 is 3-PRP! (0.000000 seconds)
3525391639439773250083+18 is 3-PRP! (0.000000 seconds)
3525391639439773250083+24 is 3-PRP! (0.000000 seconds)
3525391639439773250083+28 is 3-PRP! (0.000000 seconds)
3525391639439773250083+30 is 3-PRP! (0.000000 seconds)
3525391639439773250083+34 is  41813 · 175727 · 479797020767
3525391639439773250083+40 is  25693 · 137212144920397511
3525391639439773250083+46 is 3-PRP! (0.000000 seconds)
3525391639439773250083+48 is 3-PRP! (0.000000 seconds)
3525391639439773250083+54 is 3-PRP! (0.000000 seconds)
3525391639439773250083+58 is 3-PRP! (0.000000 seconds)
3525391639439773250083+60 is 3-PRP! (0.000000 seconds)
3525391639439773250083+66 is 3-PRP! (0.000000 seconds)
3525391639439773250083+70 is 3-PRP! (0.000000 seconds)
3525391639439773250083+76 is 3-PRP! (0.000000 seconds)


11490035915853116358673+00 is 3-PRP! (0.000000 seconds)
11490035915853116358673+04 is 3-PRP! (0.000000 seconds)
11490035915853116358673+06 is 3-PRP! (0.000000 seconds)
11490035915853116358673+10 is 3-PRP! (0.000000 seconds)
11490035915853116358673+16 is 3-PRP! (0.000000 seconds)
11490035915853116358673+18 is 3-PRP! (0.000000 seconds)
11490035915853116358673+24 is 3-PRP! (0.000000 seconds)
11490035915853116358673+28 is 3-PRP! (0.000000 seconds)
11490035915853116358673+30 is 3-PRP! (0.000000 seconds)
11490035915853116358673+34 is 3-PRP! (0.000000 seconds)
11490035915853116358673+40 is 2190756551 · 5244779896063
11490035915853116358673+46 is 3-PRP! (0.000000 seconds)
11490035915853116358673+48 is 391847 · 9577441 · 3061648823
11490035915853116358673+54 is 3-PRP! (0.000000 seconds)
11490035915853116358673+58 is 3-PRP! (0.000000 seconds)
11490035915853116358673+60 is 3-PRP! (0.000000 seconds)
11490035915853116358673+66 is 3-PRP! (0.000000 seconds)
11490035915853116358673+70 is 3-PRP! (0.000000 seconds)
11490035915853116358673+76 is 3-PRP! (0.000000 seconds)
Finetuning brought me a tiny speed up. Run the 2nd cycle now, done in 3,9h..up to number 65178316954380089460000
Collect now numbers with 5 conditions...maybe there is to the end 18/19 ???

Last fiddled with by Cybertronic on 2022-08-29 at 11:55
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Old 2022-08-29, 16:43   #28
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Searching up to 65'178'316'954'380'089'460'000 is done.
No 19-tuplet 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 19-tuplet in 1 or 2 weeks.

Last fiddled with by Cybertronic on 2022-08-29 at 17:01
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Old 2022-08-29, 21:46   #29
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There is an open question.
The unknown smallest non-trivial prime 19-tuplet have a valid 18-tuplet.


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 non-trivial known to given pattern

The first starting point is : 1906230835046648293290043
Question: Was found the other 18-tuplets in logical order or not ?!



Last fiddled with by Cybertronic on 2022-08-29 at 21:46
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Old 2022-08-30, 09:45   #30
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Got the answer.
1906230835046648293290043 is the new starting point and the other known 18-tuplets was byproducts.
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Old 2022-09-07, 05:58   #31
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CRGreathouse look for the special prime 19-tuplet 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 2022-09-07 at 06:03
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Old 2022-09-07, 17:53   #32
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Quote:
Originally Posted by Cybertronic View Post
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.
How do I get Big-Int overload.bi?
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Old 2022-09-07, 18:27   #33
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Default Big Int

Quote:
Originally Posted by CRGreathouse View Post
How do I get Big-Int overload.bi?

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 sieve-ranges.
Attached Files
File Type: txt Big-Int overload.txt (28.8 KB, 22 views)

Last fiddled with by Cybertronic on 2022-09-07 at 18:34
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