The following rare solutions were found in the project

17-tuples

4679308425291971279: 0 12 30 54 72 144 180 252 282 312 384 420 492 510 534 552 564
4787657908465021067: 0 36 90 156 216 240 246 294 330 366 414 420 444 504 570 624 660
6031294806199243111: 0 6 18 48 60 108 126 150 318 486 510 528 576 588 618 630 636
6254294998011830071: 0 30 42 60 96 102 120 180 246 312 372 390 396 432 450 462 492

24-tuples

4686452527338185687: 0 26 42 84 146 150 186 194 210 234 326 416 420 510 602 626 642 650 686 690 752 794 810 836
5179852391836338883: 0 6 16 34 64 66 108 174 198 214 220 226 288 294 300 316 340 406 448 450 480 498 508 514
5367691788896274911: 0 50 72 78 132 168 206 248 258 288 300 318 320 338 350 380 390 432 470 506 560 566 588 638
5498259426448114709: 0 18 50 60 74 78 92 104 108 110 162 204 248 290 342 344 348 360 374 378 392 402 434 452
5821555215042148069: 0 12 34 88 132 160 192 208 228 252 258 262 330 334 340 364 384 400 432 460 504 558 580 592
5992831885521587569: 0 72 88 112 114 130 144 154 168 192 222 240 262 280 310 334 348 358 372 388 390 414 430 502
6084429360777261647: 0 80 90 152 182 186 242 252 272 356 360 416 426 482 486 570 590 600 656 660 690 752 762 842
6088107348398350579: 0 64 154 160 210 250 274 292 342 358 370 414 538 582 594 610 660 678 702 742 792 798 888 952
6109180764555243559: 0 4 10 18 22 42 52 78 84 94 172 178 204 210 288 298 304 330 340 360 364 372 378 382
6116852902194972481: 0 10 12 18 78 136 172 178 192 258 328 342 376 390 460 526 540 546 582 640 700 706 708 718

26-tuple

5179852391836338871: 0 12 18 28 46 76 78 120 186 210 226 232 238 300 306 312 328 352 418 460 462 492 510 520 526 538

This is the only 26-tuple known at the moment.
This is a symmetric tuple of consecutive primes of the longest length that is known.

16-tuples consisting of twins

4712997307944436787: 0 2 12 14 42 44 90 92 132 134 180 182 210 212 222 224
5512467165717387017: 0 2 30 32 42 44 72 74 132 134 162 164 174 176 204 206
6012492175914927431: 0 2 66 68 150 152 180 182 276 278 306 308 390 392 456 458
6118066623221589779: 0 2 30 32 42 44 72 74 78 80 108 110 120 122 150 152
6235347969661701029: 0 2 42 44 72 74 192 194 198 200 318 320 348 350 390 392

I would like to remind you that rare solutions found in the BOINC project TBEG are available here
https://boinc.tbrada.eu/spt/explore.php?rare

Rare solutions have also been found

17-tuples

6239488505247755519: 0 12 42 60 102 138 198 210 240 270 282 342 378 420 438 468 480
6561013649263688341: 0 30 42 60 90 156 210 270 276 282 342 396 462 492 510 522 552

24-tuples

6276097306527637499: 0 54 72 120 144 198 254 270 278 380 392 410 432 450 462 564 572 588 644 698 722 770 788 842
6699048341794868749: 0 4 18 22 48 60 114 162 202 228 250 280 342 372 394 420 460 508 562 574 600 604 618 622

https://boinc.termit.me/adsl/spt_explore.php?rare