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Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Deprecated: Creation of dynamic property BoincUser::$nposts is deprecated in /var/boincadm/prj/html/inc/forum.inc on line 613 Posts: 667 Credit: 432,784 RAC: 0 
From the results posted by Natalia and me, it looks like A113274 is incomplete  missing some terms in the middle. Second, it is clear that searching for just the largest gap is not going to cut it. If we want to extend the sequence, we want a monotonic sequence of TPT with increasing gap. So that requires one more modification to the App and Asim. Also the largest gap is going to increase forever as the primes get bigger. Edit: A113274 is not wrong, it deals with not strictly consecutive twin primes. Eg: it can contain (41,43) (59,61) even though there are two primes in between the twins. I think that the SPT and STPT&TPT applications should work separately, because they will work in different ranges. Not necessary. I can use batch numbers for the separation. I still need to benchmark it, but the addition of stpt&tpt search has little impact on the speed. 
Natalia Makarova Project scientist Send message Joined: 8 Feb 19 Deprecated: Creation of dynamic property BoincUser::$nposts is deprecated in /var/boincadm/prj/html/inc/forum.inc on line 613 Posts: 423 Credit: 0 RAC: 0 
Here is sequence of ever increasing gaps between consecutive twin pairs. Also found [209241428699, 209241428701, 209241429071, 209241429073] 372 Thank you for confirming the sequence. Now you can create a sequence in OEIS. 
Natalia Makarova Project scientist Send message Joined: 8 Feb 19 Posts: 423 Credit: 0 RAC: 0 
The "gaps between twin primes" problem is presented in three OEIS sequences 1) https://oeis.org/A113275 A113275 Lesser of twin primes for which the gap before the following twin primes is a record. 2) https://oeis.org/A036063 A036063 Increasing gaps among twin primes: size. 3) https://oeis.org/A113274 A113274 Record gaps between twin primes. Our sequence can also be represented in three variants. All data for the three sequences is contained here twin_gap_seq: 
Natalia Makarova Project scientist Send message Joined: 8 Feb 19 Posts: 423 Credit: 0 RAC: 0 
A sequence similar to A113274 can be called “Rising gaps between of consecutive twin primes”. This sequence has the form 2, 6, 12, 18, 30, 36, 54, 72, 102, 108, 126, 132, 138, 150, 186, 198, 210, 240, 246, 252, 282, 288, 294, 306, 312, 318, 342, 348, 372 I think it’s not worth creating a sequence similar to A036063, because these are the essence of the reduced by 2 members of the previous sequence 0, 4, 10, 16, 28, 34, 52, 70, 100, 106, 124, 130, 136, 148, 184, 196, 208, 238, 244, 250, 280, 286, 292, 304, 310, 316, 340, 346, 370 A sequence similar to A113275 is, of course, needed. This sequence has the following form 3, 5, 137, 1931, 2969, 20441, 48677, 173357, 838247, 4297091, 14982551, 30781187, 34570661, 43891037, 79167731, 875971469, 1209266801, 2505898931, 3399081821, 5002002407, 13600912607, 28261373771, 31120423097, 31153871741, 44725020167, 59120474339, 70906853447, 143334302009, 209241428699 
Natalia Makarova Project scientist Send message Joined: 8 Feb 19 Posts: 423 Credit: 0 RAC: 0 
O! I found in OEIS the sequence I made up. https://oeis.org/A329165 A329165 Let P1, P2, P3, P4 be consecutive primes with P2P1=P4P3=2. a(n)=(P3P1)/6 when the length of the gap with no primes between the two pairs of twin primes sets a record. 1, 2, 3, 5, 6, 9, 12, 17, 18, 21, 22, 23, 25, 31, 33, 35, 40, 41, 42, 47, 48, 49, 51, 52, 53, 57 Why all gaps divided by 6? Compare with my sequence 2, 6, 12, 18, 30, 36, 54, 72, 102, 108, 126, 132, 138, 150, 186, 198, 210, 240, 246, 252, 282, 288, 294, 306, 312, 318, 342, 348, 372 There is no first term because the first two twins (3,5) and (5,7) intersect. Next, all the members of my sequence (except 348 and 372) are in the sequence A329165 as a(n)/6. Until I found the corresponded sequence of twins primes 5, 137, 1931, 2969, 20441, 48677, 173357, 838247, 4297091, 14982551, 30781187, 34570661, 43891037, 79167731, 875971469, 1209266801, 2505898931, 3399081821, 5002002407, 13600912607, 28261373771, 31120423097, 31153871741, 44725020167, 59120474339, 70906853447, 143334302009, 209241428699 Maybe there is such a sequence too. The search in OEIS is endless! So, we will continue the sequence A329165. In this sequence, there are now only 26 members. We have two more members: a(27) = 58 a(28) = 62. PS. Entering such a sequence 5, 137, 1931, 2969, 20441, 48677 in the OEIS search field did not find anything. 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
Batch 55 stpt: testing more of the application. It looks there are still some errors. 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
I think I solved the last outstanding issue in the application and we can move forwards. This will involve either resubmitting previous regular batch to compare results. Or move into new area in multiple directions at the same time: 1) continue search for symmetric prime tuples 2) start new search for symmetric and asymmetric twin prime tuples, and twin prime gaps We could 3) resubmit all of the previous search in the 5e176e17 range with the new application: not only that would find the TPT, STPT and twin gaps in the interval, but also verify results from the manual and automatic search at very little additional cost. There is some work still left on the backend: 4) Benchmark the new app and edit credit multiplier. 5) Fix how twin gap data is inserted into DB. Currently redundant, but not duplicate, entries are inserted. 6) Rerun the assimilator on the whole result database due to format changes. 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
Batch 56: 530051407000000000 .. 545771407000000000 1 Count: 8000 Continue with the new application 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
Parameters for further search must be verified or refined. Currently they are:

Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
Besides twin primes, there also exist cousin primes and sexy primes. Both cousin (d=4) and twin (d=2) do not intersect or touch themselves greater than 7. My program exploits this property for twin primes. It could be easily extended to look for cousin prime tuples as well. But sexy primes (d=6) are harder, since they can can form up to quadruplets. Also when we start looking for cousin prime tuples, or sexy prime tuples, we could start looking for various combinations of twin and cousin primes and that will get messy quickly. Is there a motivation? 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
Batch 57: 545771407000000000 .. 577211407000000000 1 Count: 16000 Continue with the new application 
Natalia Makarova Project scientist Send message Joined: 8 Feb 19 Posts: 423 Credit: 0 RAC: 0 
I think we need to limit ourselves to finding twins. Where can I see the results for the twins for k=6 (12tuple) and k=7 (14tuple)? I found only this https://boinc.tbrada.eu/spt_list.php?k=12 . . . . . . . 999475912613: 0 26 38 66 68 96 110 138 140 168 180 206 999476523211: 0 12 18 22 36 52 96 112 126 130 136 148 999723054251: 0 6 26 36 48 60 98 110 122 132 152 158 999801043721: 0 2 12 32 72 78 110 116 156 176 186 188 999930089267: 0 2 20 32 44 54 62 72 84 96 114 116 999933514397: 0 12 30 60 110 114 152 156 206 236 254 266 999938914729: 0 10 24 60 82 84 100 102 124 160 174 184 999954513763: 0 18 58 60 76 148 168 240 256 258 298 316 999982936349: 0 14 18 50 68 78 80 90 108 140 144 158 532905152025296537: 0 2 54 56 60 62 84 86 90 92 144 146 533308875499369997: 0 2 24 26 30 32 54 56 60 62 84 86 541024702436824187: 0 2 30 32 114 116 150 152 234 236 264 266 541267134297120527: 0 2 30 32 72 74 132 134 174 176 204 206 # last = 331678 # count = 15036 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
I quickly created two pages, but I am working on better page to explore the database. https://boinc.tbrada.eu/spt_list_stpt.php?k=8  symmetric tuples of twin primes (k is number of primes) https://boinc.tbrada.eu/tpt_list.php?k=9  asymmetric tuples of twin primes (k is number of pairs) All STPTs are included in SPT list as well. 
Natalia Makarova Project scientist Send message Joined: 8 Feb 19 Posts: 423 Credit: 0 RAC: 0 
# Copyright Tomas Brada, ask on forum about reuse or citation. # where kind = tpt # where k = 9 532359367138961447: 0 2 42 44 72 74 114 116 192 194 252 254 330 332 402 404 444 534790455001337861: 0 2 216 218 240 242 258 260 300 302 306 308 366 368 396 398 516 535474368412823759: 0 2 162 164 348 350 372 374 390 392 402 404 540 542 570 572 672 536706305502981749: 0 2 78 80 120 122 282 284 438 440 510 512 522 524 588 590 672 539203083290572667: 0 2 30 32 42 44 72 74 150 152 324 326 390 392 414 416 432 541603519435938941: 0 2 48 50 78 80 126 128 288 290 300 302 330 332 456 458 480 545690807892680447: 0 2 30 32 84 86 90 92 180 182 312 314 324 326 450 452 504 574215423057543257: 0 2 12 14 102 104 144 146 180 182 222 224 282 284 312 314 324 574866882160551047: 0 2 12 14 42 44 60 62 84 86 90 92 114 116 240 242 270 576401886649823237: 0 2 42 44 90 92 120 122 150 152 222 224 390 392 432 434 474 576790168452150197: 0 2 42 44 54 56 84 86 240 242 270 272 450 452 462 464 492 # last = 486160 # count = 11Excellent! Please see these sequences in OEIS https://oeis.org/A087641 A087641 Start of the first sequence of exactly n consecutive pairs of twin primes. https://oeis.org/A259034 A259034 Start of a string of exactly 9 consecutive (but disjoint) pairs of twin primes. We have for k=9 a large missed interval (1980326398382819, 532359367138961447). Similarly for k=8. See https://oeis.org/A263205 A263205 Start of a string of exactly 8 consecutive (but disjoint) pairs of twin primes. 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
The reason there are no new tasks for SPT, is because there is a problem with STPT detection code. I identified the problem, but need to verify that it works and does not affect anything else. 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
Batch 58: 577211407000000000 .. 600001477000000000 1 Count: 11598 Continue with the new application 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
There is a very large number of STPT(8) (4 pairs), over 2 million and it was slowing the assimilator quite a lot. So, I disabled saving those into the tuple database. The result files, remain intact and archived for later use. 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
List of OEIS sequences for new search interval: https://oeis.org/A087641 TPT(N) https://oeis.org/A035795 TPT(7) https://oeis.org/A263205 TPT(8) https://oeis.org/A259034 TPT(9) https://oeis.org/A274792 STPT(n) https://oeis.org/A330278 STPT(12) https://oeis.org/A175309 SPT(N) ? https://oeis.org/A055382 ...? https://oeis.org/A113274, https://oeis.org/A113275 twin_gaps https://oeis.org/A329164, https://oeis.org/A329165 twin_gaps https://oeis.org/A256234 4x4 Missing sequences for STPT and SPT. I will add later. 
Tomáš Brada Project administrator Volunteer developer Send message Joined: 3 Feb 19 Posts: 667 Credit: 432,784 RAC: 0 
Batch 59: 5 .. 1000000000005 1 Count: 100 Scan beginning with new App. inp.mine_k= 14; inp.mino_k= 9; inp.max_k= 64; inp.upload = 0; inp.exit_early= 0; inp.out_last_primes= 0; inp.out_all_primes= 0; inp.primes_in.clear(); inp.twin_k=6; inp.twin_min_k=8; inp.twin_gap_k=255; inp.twin_gap_min=249; inp.twin_gap_kmin=75; wu.delay_bound = 4 * 3600; 
Natalia Makarova Project scientist Send message Joined: 8 Feb 19 Posts: 423 Credit: 0 RAC: 0 
We have the sequence https://oeis.org/A113274 and the corresponding sequence https://oeis.org/A113275. We have the sequence https://oeis.org/A329165, but we do not have the corresponding sequence with real values of the twins primes. I found the first terms of this sequence 5, 137, 1931, 2969, 20441, 48677, 173357, 838247, 4297091, 14982551, 30781187, 34570661, 43891037, 79167731, 875971469, 1209266801, 2505898931, 3399081821, 5002002407, 13600912607, 28261373771, 31120423097, 31153871741, 44725020167, 59120474339, 70906853447, 143334302009, 209241428699 Tomáš Brada please create this sequence first. Indicate authorship and the link to the results https://boinc.tbrada.eu/forum_thread.php?id=3055&postid=3915#3915 Then there will be the results of the TBEG project. PS. I did not find such a sequence in OEIS. But maybe I was looking badly? 
©2024 Tomáš Brada