Prime p₀= 2813715822105266861 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 82 2 178 2 4 2 28 2 10 2 (?)
a_n: 0 2 96 98 180 182 360 362 366 368 396 398 408 410
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 410
Found by: [SG-FC] hl
db: batch=82, k=14, 94 82 178 4 28 10

SPT(20)	2813714646168459217	0 4 6 16 34 60 84 100 114 142 144 172 186 202 226 252 270 280 282 286	-1175936807644
STPT(10)	2813714978584424669	0 2 18 20 30 32 42 44 60 62	-843520842192
SPT(16)	2813715215429644261	0 10 16 42 52 82 102 108 130 136 156 186 196 222 228 238	-606675622600
SPT(16)	2813715332356668863	0 90 116 140 168 180 198 236 258 296 314 326 354 378 404 494	-489748597998
STPT(10)	2813715473975287559	0 2 18 20 30 32 42 44 60 62	-348129979302
SPT(16)	2813715529947446041	0 16 42 58 60 78 130 142 156 168 220 238 240 256 282 298	-292157820820
STPT(10)	2813716403614506389	0 2 18 20 30 32 42 44 60 62	581509239528
SPT(16)	2813716510754216791	0 6 12 28 40 52 142 168 190 216 306 318 330 346 352 358	688648949930
SPT(18)	2813716540698460297	0 40 52 102 162 190 192 262 286 390 414 484 486 514 574 624 636 676	718593193436
TPT(14)	2813716837943984381	0 2 48 50 126 128 168 170 300 302 318 320 336 338	1015838717520
SPT(16)	2813716873169378213	0 24 50 60 78 90 134 206 228 300 344 356 374 384 410 434	1051064111352