Symmetric Prime Tuples development

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Profile Tomáš Brada
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Message 3664 - Posted: 16 Oct 2019, 15:08:42 UTC

let k=7
tuple is (a1,a2,a3,a4,a5,a6,a7)
a1+a7=a2+a6=a3+a5=2a4
but in the program, we have access to tuple in another form:
(d1,d2,d3,d4,d5,d6,d7), where ai=a[i-1]+di and d1 is ignored
a1+a7=a2+a6 <=> a1-a2=a6-a7 <=> d2=d7
a2+a6=a3+a5 <=> a2-a3=a5-a6 <=> d3=d6
This was checked so far. But I forgot the last term:
a3+a5=2a4 <=> a3-a4=a4-a5 <=> d4=d5
Double check with another equation
a1+d2+d3+a1+d2+d3+d4+d5 = 2(a1+d2+d3+d4) <=>
2a1+2d2+2d3+d4+d5 = 2a1+2d2+2d3+2d4 <=>
d4=d5
That is d[floor((k+1)/2)]=d[floor((k+1)/2)+1].

So, I adjusted the loop condition in the program.
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Message 3665 - Posted: 16 Oct 2019, 15:26:22 UTC

Batch 44, range 500304494994471000..500309661688072493 with the new app.
Two k=18 tuples expected in that range.
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Message 3666 - Posted: 16 Oct 2019, 15:36:24 UTC

Batch 43, k=16:
500266350516360713
500267143507426063
500267781202358707
500267781202358707
500268284871559733
500268284871559733
500268843535863161
500269145781632167
500269234162105211
500270446647461549
500270737840432687
500270748390212087
500270751465263417
500271448968878617
500271943304408983
500272080614138927
500272607972401211
500272700245273201
500272700245273201
500272700528288777
500272700528288777
500272793205171263
500272793205171263
500273028468009427
500273827425330443
500274166044532933
500274166044532933
500274274865948021
500274909812441759
500275250999654981
500275543575861041
500275715671566853
500278186279212983
500278335502574543
500278583288499619
500279036468361203
500279109967926193
500279542202838913
500280450218473861
500280564172703627
500280564172703627
500280896805596233
500280896805596233
500281289472391067
500281563521867189
500282008739579683
500282008739579683
500282872181452511
500284020809152127
500284077687278369
500284160837133779
500284240074267293
500284240074267293
500285021738317531
500285464203990529
500285562164947987
500286087573004753
500286087573004753
500286232105124473
500286427453737347
500286766859602783
500286766859602783

k=18:
500278335502574539
500285021738317523


Not found by Xaver, but found by batch 43:
500267781202358707
500268284871559733
500272700245273201
500272700528288777
500272793205171263
500274166044532933
500280564172703627
500280896805596233
500282008739579683
500284240074267293
500286087573004753
500286766859602783
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Natalia Makarova
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Message 3667 - Posted: 16 Oct 2019, 16:17:45 UTC - in response to Message 3666.  

Not found by Xaver, but found by batch 43: ...

These are duplicates

500267781202358707
500267781202358707

500268284871559733
500268284871559733

500272700245273201
500272700245273201

500272700528288777
500272700528288777

500272793205171263
500272793205171263

500274166044532933
500274166044532933

500280564172703627
500280564172703627

500280896805596233
500280896805596233

500282008739579683
500282008739579683

500284240074267293
500284240074267293

500286087573004753
500286087573004753

500286766859602783
500286766859602783
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Message 3668 - Posted: 16 Oct 2019, 19:33:57 UTC - in response to Message 3667.  

Not found by Xaver, but found by batch 43: ...

These are duplicates

Oh, look at that! BOINC just loves sending duplicate tasks.
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Message 3669 - Posted: 17 Oct 2019, 6:18:04 UTC

Batch 44:
500304494994472001      16
500305859582509297      16
500306257013490029      16
500306578361527807      16
500306743084607153      16
500307433730800667      16
500307463433944237      16
500307833181597457      16
500308889307138697      16
500309438916670223      16
500309569397326103      16
500309661433256557      16
500309661688072493      16
500309678813750107      16
500306743084607131      18
500309661433256551      18

Sorry for the bad format, I will improve it.
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Message 3670 - Posted: 17 Oct 2019, 9:56:27 UTC - in response to Message 3669.  

Solution of Batch 44, matches solution by Xaver. Success.
I think I can load next batch with 8000 tasks and start interactive beta.
Windows app will be on Saturday.
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Message 3671 - Posted: 17 Oct 2019, 13:42:43 UTC - in response to Message 3670.  
Last modified: 17 Oct 2019, 13:46:08 UTC

Solution of Batch 44, matches solution by Xaver. Success.
I think I can load next batch with 8000 tasks and start interactive beta.
Windows app will be on Saturday.

Fine!

What interval is contained in one WU?
Will you have automatic tasks generation?
Is it possible to access the results file, as in the PADLS TOTAL subproject?
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Message 3672 - Posted: 17 Oct 2019, 15:46:02 UTC - in response to Message 3671.  

Results are now online! File updated instantly.
https://boinc.tbrada.eu/spt_list.php?batch=44
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Message 3675 - Posted: 18 Oct 2019, 20:26:12 UTC

Batch 45 range 501000000000000000..501300133640000000.
2922 wu, interval 102680000000 per wu.
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Message 3679 - Posted: 19 Oct 2019, 10:30:42 UTC - in response to Message 3675.  
Last modified: 19 Oct 2019, 10:38:06 UTC

Batch 45 range 501000000000000000..501300133640000000.
2922 wu, interval 102680000000 per wu.

On my PC, the first WU miscalculated for 15 minutes

Поиск ассоциативных наборов простых              0:15:40
Текущий интервал: [501000107999928808 ... 501000109999928808]
Просеяно  :      0%
Скорость  :    411
Найдено 16:      0
Найдено 17:      0
Найдено 18:      0
Найдено 19:      0
Найдено 20:      0

Tomáš Brada
Do you take into account that some tuples may be at the junction of two intervals?
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Message 3681 - Posted: 19 Oct 2019, 12:21:32 UTC - in response to Message 3679.  

Do you take into account that some tuples may be at the junction of two intervals

Yes this is handled. Each wu generates some more primes (32) at the end of interval to make sure all possible tuples are found.
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Message 3682 - Posted: 19 Oct 2019, 14:16:52 UTC
Last modified: 19 Oct 2019, 14:42:45 UTC

I already see the solutions!

k=18
501024972150015263: 0 30 56 68 74 98 140 144 240 254 350 354 396 420 426 438 464 494
501072867640004549: 0 74 92 114 120 140 182 200 242 252 294 312 354 374 380 402 420 494
501087687723058409: 0 18 24 42 44 128 164 212 284 288 360 408 444 528 530 548 554 572
501118645803494903: 0 18 20 66 120 158 170 176 186 188 198 204 216 254 308 354 356 374
501156574540472371: 0 16 28 72 108 120 136 138 148 240 250 252 268 280 316 360 372 388
501202194563468971: 0 18 28 66 108 130 138 166 178 210 222 250 258 280 322 360 370 388
501207471897602941: 0 6 22 30 72 106 120 136 160 228 252 268 282 316 358 366 382 388
501276864604781789: 0 24 30 44 62 68 84 128 150 212 234 278 294 300 318 332 338 362
501296612968836119: 0 24 44 74 78 92 114 164 180 182 198 248 270 284 288 318 338 362
k=20
501072867640004521: 0 28 102 120 142 148 168 210 228 270 280 322 340 382 402 408 430 448 522 550

https://boinc.tbrada.eu/spt_list.php?batch=45

Fine!
Bravo, Tomáš!

Thanks to our helpers!
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Message 3686 - Posted: 19 Oct 2019, 20:13:28 UTC

Compiled app for windows. There was a small error with atomic file writing. More specifically, it is impossible to update file safely so that either the old or the new version will remain after a system crash on windows. So I had to revert to unsafe checkpoint writing. That is also the reason while crash/power failure during windows update will really mess up the system.
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Message 3688 - Posted: 19 Oct 2019, 20:16:47 UTC - in response to Message 3686.  

5843 More workunits submitted. Up to 501900195560000000.
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Message 3692 - Posted: 21 Oct 2019, 10:25:44 UTC

In the file https://boinc.tbrada.eu/spt_list.php?batch=45
errors are noticed
501418562132535539: 0 8 24 42 74 2647 6231 19543 31319 44631 48215 50788 50820 50838 50854 50862
501718014215426237: 0 12 26 2599 4135 7719 13863 16935 20007 23079 29223 32807 34343 36916 36930 36942


It should be right
501418562132535539: 0 8 24 42 74 84 98 150 452 504 518 528 560 578 594 602
501718014215426237: 0 12 26 36 42 56 80 92 360 372 396 410 416 426 440 452
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Message 3693 - Posted: 21 Oct 2019, 11:52:32 UTC

Can any non-mathematician read this "result" page ?? :)

And also : it does not seem to be linked to the computer/member who "found" the "result", correct ?

Like Primegrid is doing each time an interesting (and significant) result is found : it is a very big incentive for many crunchers to participate to projects (same as badges).
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Message 3694 - Posted: 21 Oct 2019, 12:47:03 UTC - in response to Message 3693.  
Last modified: 21 Oct 2019, 12:55:57 UTC

Can any non-mathematician read this "result" page ?? :)

Yes. Please read out this page
https://en.wikipedia.org/wiki/Prime_k-tuple
I can also recommend the page
http://www.primepuzzles.net/problems/prob_062.htm
if anyone wants to know more.

And also : it does not seem to be linked to the computer/member who "found" the "result", correct ?

No interesting solutions have been found yet.
Tomáš Brada can talk about the opportunity to find the author of an interesting solution.
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Message 3701 - Posted: 21 Oct 2019, 15:15:16 UTC - in response to Message 3692.  

Now back to the topic.
In the file https://boinc.tbrada.eu/spt_list.php?batch=45
errors are noticed
501418562132535539: 0 8 24 42 74 2647 6231 19543 31319 44631 48215 50788 50820 50838 50854 50862
501718014215426237: 0 12 26 2599 4135 7719 13863 16935 20007 23079 29223 32807 34343 36916 36930 36942


It should be right
501418562132535539: 0 8 24 42 74 84 98 150 452 504 518 528 560 578 594 602
501718014215426237: 0 12 26 36 42 56 80 92 360 372 396 410 416 426 440 452


There are actually two such entries already! Something is wrong.

Querying the database for them:
+--------------------+----+-------------------------------------+
| start              | k  | ofs                                 |
+--------------------+----+-------------------------------------+
| 501418562132535539 | 16 | 8 16 18 32 2573 3584 13312 11776    |
| 501718014215426237 | 16 | 12 14 2573 1536 3584 6144 3072 3072 |
+--------------------+----+-------------------------------------+

I was hoping there would be another, good, copy of the result but there isn't. The validator does not check wheter the numbers are prime, so the error was not caught. But we should at least do a simple test whether all the differences are even. The first entry blows up on 5 th number with 2573 and the second on 3 rd with, again, 2573. I do not know why it failed.

Moreover there are many invalid results and also many results that failed. Many of the failed results fail to read the input file.
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Message 3702 - Posted: 21 Oct 2019, 15:43:04 UTC

Not ok. Basically, the error that came up when compiling tot5 app for windows struck again. While developing on windows, I did not commit the changed needed to fix the issue. And when I was creating SPT app, I thought I had the fixed code available so I incorporated it straight away. But it was missing the fix.
So now I had to disable the windows app and abort 1030 in-progress windows results. I also had to invalidate results worth of 73967 credits. The assigned credits were not removed.
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