Prime p₀= 2088946831289212691 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 136 2 40 2 34 2 70 2 70 2 (?)
a_n: 0 2 60 62 198 200 240 242 276 278 348 350 420 422
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: 422
Found by: Landjunge
db: batch=80, k=14, 58 136 40 34 70 70

TPT(14)	2088945233847372869	0 2 42 44 78 80 168 170 180 182 330 332 348 350	-1597441839822
SPT(16)	2088945253010550169	0 54 124 148 184 190 198 202 210 214 222 228 264 288 358 412	-1578278662522
SPT(16)	2088946095855637523	0 60 68 84 114 134 140 198 290 348 354 374 404 420 428 488	-735433575168
SPT(16)	2088946141775278103	0 8 26 36 48 86 114 140 204 230 258 296 308 318 336 344	-689513934588
SPT(18)	2088946287054704611	0 6 70 100 112 160 232 238 286 312 360 366 438 486 498 528 592 598	-544234508080
STPT(12)	2088946803505052327	0 2 12 14 42 44 102 104 132 134 144 146	-27784160364
SPT(16)	2088946960566160963	0 130 154 178 190 234 246 256 318 328 340 384 396 420 444 574	129276948272
SPT(16)	2088947398699442227	0 22 30 36 42 52 126 150 196 220 294 304 310 316 324 346	567410229536
STPT(10)	2088947436364182809	0 2 18 20 30 32 42 44 60 62	605074970118
SPT(16)	2088948113523878989	0 28 64 72 82 132 154 160 252 258 280 330 340 348 384 412	1282234666298
SPT(13)	2088948532569209197	0 12 60 90 102 120 132 144 162 174 204 252 264	1701279996506