This tuple was probably found by nenym. Lucky one!

This is a Christmas present :)

My archive has the following 24-tuples

22930603692243271: 0 70 76 118 136 156 160 178 202 222 238 250 378 390 406 426 450 468 472 492 510 552 558 628
34984922852185283: 0 26 66 74 80 96 104 126 204 206 216 236 258 278 288 290 368 390 398 414 420 428 468 494
60960572612579749: 0 30 58 64 72 82 84 102 120 154 160 174 238 252 258 292 310 328 330 340 348 354 382 412
481408770994035947: 0 20 54 60 72 86 90 110 132 210 222 242 264 284 296 374 396 416 420 434 446 452 486 506
492720459594614777: 0 30 32 54 80 110 164 180 204 234 264 282 374 392 422 452 476 492 546 576 602 624 626 656
675424273001524577: 0 12 24 26 60 72 110 126 152 156 186 200 306 320 350 354 380 396 434 446 480 482 494 506
678456599278876927: 0 12 36 66 70 126 130 192 202 214 274 300 376 402 462 474 484 546 550 606 610 640 664 676
794297921067358991: 0 6 12 38 86 98 126	210 216 306 308 318 320 330 332 422 428 512 540 552 600 626 632 638

Perhaps, several tuples found in the Stop@home project are missing.

26-tuple is still unknown!

I started working on application to search for symmetric and not-symmetric tuples of twin primes.

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I started working on application to search for symmetric and not-symmetric tuples of twin primes.

Fine!
XAVER fills the OEIS A330278 sequence.
I also have several solutions for this sequence.

I am looking for a second symmetric 14-tuples from twin primes.
I do not yet work with not-symmetric tuples.

Just to verify that i did not introduce problems, searching for spt k=5:

T 500100101650071059(5): 18 42 42
T 500100101650397459(5): 18 42 42

that is:
500100101650071059: 0 18 60 102 120
500100101650397459: 0 18 60 102 120

Also
T 500100101684488021(7): 78 60 12 12
500100101684488021: 0 78 138 150 162 222 300

Some twin prime tuples (asymetric):
W 500100101711358227(5): 70 88 148 28
W 500100101958716447(5): 10 46 178 22
that is
500100101711358227: 0 2 70 72 162 164 312 314 342 344
500100101958716447: 0 2 10 12 58 60 238 240 262 264

I will keep the accepted format for output, but in database, the short format is used.

OEIS evolving sequences of non-symmetric tuples from consecutive pairs of twin primes

1. Start of a string of exactly 7 consecutive (but disjoint) pairs of twin primes.
https://oeis.org/A035795
2. Start of a string of exactly 8 consecutive (but disjoint) pairs of twin primes.
https://oeis.org/A263205
3. Start of a string of exactly 9 consecutive (but disjoint) pairs of twin primes.
https://oeis.org/A259034

And also for k>9, such sequences are not yet in OEIS.

OEIS evolving sequence of symmetric tuples from consecutive pairs of twin primes

Primes starting 12-tuples of consecutive primes that have symmetrical gaps about their mean and form 6 pairs of twin primes.
https://oeis.org/A330278

And also for k>12 (or k>6 pairs), such sequences are not yet in OEIS.

More than 10,000 members in the sequence are not required to be searched.
Of course, less is possible.

Group of 7 consecutive twin primes
500308655992846037: k=7 52 148 4 40 118 16

Group of 7 consecutive twin primes
500308655992846037: k=7 52 148 4 40 118 16

Yes, the asymmetric tuple, unfolded

[500308655992846037, 500308655992846039, 500308655992846091, 500308655992846093,
500308655992846241, 500308655992846243, 500308655992846247, 500308655992846249,
500308655992846289, 500308655992846291, 500308655992846409, 500308655992846411,
500308655992846427, 500308655992846429]

Suitable for sequence Start of a string of exactly 7 consecutive (but disjoint) pairs of twin primes.

Results from the new application are valid and identical to the reference batch.
And another asymmetric 7: W 500306715408864029(7): 28 40 46 28 10 58

Todo: add check for largest distance between twins.

Todo: add check for largest distance between twins.

My current maximum is 214

2184916780531349: 0 2 18 20 42 44 258 260 282 284 300 302

Todo: Optimize the palindrome search. Number of comparisons can be reduced by checking the center pair (even+odd) first.

Note: every symmetric k-tuple is also a symmetric (k-2)-tuple.
Question: Should the smaller tuples derived from larger tuple also appear in the results?

Note: every symmetric k-tuple is also a symmetric (k-2)-tuple.
Question: Should the smaller tuples derived from larger tuple also appear in the results?

Yes, they are appearing now.

Example

528050771271601399: 0 22 48 52 82 90 94 112 120 138 142 150 180 184 210 232
528050771271601393: 0 6 28 54 58 88 96 100 118 126 144 148 156 186 190 216 238 244
528050771271601327: 0 66 72 94 120 124 154 162 166 184 192 210 214 222 252 256 282 304 310 376
528050771271601321: 0 6 72 78 100 126 130 160 168 172 190 198 216 220 228 258 262 288 310 316 382 388
528050771271601307: 0 14 20 86 92 114 140 144 174 182 186 204 212 230 234 242 272 276 302 324 330 396 402 416

I think this should be so in the future.

Note: every symmetric k-tuple is also a symmetric (k-2)-tuple.
Question: Should the smaller tuples derived from larger tuple also appear in the results?

Yes, they are appearing now.
I think this should be so in the future.

I am working on the application code currently. With the optimization to the application, only the largest tuple is reported. Should I work extra to also report the smaller tuples as well?

I am working on the application code currently. With the optimization to the application, only the largest tuple is reported. Should I work extra to also report the smaller tuples as well?

It will be inconvenient for me.
For example, I will not have a full database for 16-tuples, but I have to work constantly with these tuples (search for squares).

In general, it is better to have a complete database for each k.
So it was in the original program by Belyshev.
I see no reason to change this.

I got the program working!

525725685000000000..525725686026800003
nprime: 25165023
primes:
tuples:
T 525725685482103023(12): 8 30 42 18 10 110
twins:
W 525725685315463739(6): 10 16 88 16 10
twin_tuples:
U 525725685041603087(8): 2 28 2 22
U 525725685145432661(8): 2 28 2 76
U 525725685315463669(16): 10 60 2 10 2 16 2 88
U 525725685432929519(8): 2 28 2 10
twin_cnt:
status: 1
sieve_init_ms720

To make it convenient for you: The validator will insert the smaller tuples from one larger into the database, so the database of k-tuples can be complete.

todo: check this: W 525725685315463739(6): 10 16 88 16 10