Prime p₀= 2157999008525647589 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 76 2 46 2 40 2 28 2 118 2 (?)
a_n: 0 2 42 44 120 122 168 170 210 212 240 242 360 362
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: 362
Found by: Landjunge
db: batch=81, k=14, 40 76 46 40 28 118

SPT(16)	2157998116024554311	0 18 26 56 68 110 126 138 200 212 228 270 282 312 320 338	-892501093278
SPT(16)	2157998184865311563	0 54 60 78 146 168 186 188 216 218 236 258 326 344 350 404	-823660336026
STPT(10)	2157998248194471971	0 2 36 38 78 80 120 122 156 158	-760331175618
STPT(10)	2157998717225126981	0 2 6 8 18 20 30 32 36 38	-291300520608
SPT(16)	2157998838220844537	0 72 74 150 164 206 240 266 270 296 330 372 386 462 464 536	-170304803052
STPT(10)	2157998900049469949	0 2 42 44 90 92 138 140 180 182	-108476177640
STPT(10)	2157999289082533241	0 2 36 38 78 80 120 122 156 158	280556885652
SPT(16)	2157999577375218053	0 50 60 66 96 126 176 180 224 228 278 308 338 344 354 404	568849570464
SPT(16)	2157999909163584791	0 56 68 86 158 170 252 258 320 326 408 420 492 510 522 578	900637937202
SPT(16)	2157999993915490807	0 24 34 64 76 106 154 162 244 252 300 330 342 372 382 406	985389843218
SPT(18)	2158000251804142201	0 40 42 60 106 148 162 222 228 250 256 316 330 372 418 436 438 478	1243278494612