Prime p₀= 3997484870743714121 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 40 2 34 2 58 2 100 2 76 2 (?)
a_n: 0 2 48 50 90 92 126 128 186 188 288 290 366 368
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: 368
Found by: [AF] Kalianthys
db: batch=84, k=14, 46 40 34 58 100 76

SPT(16)	3997482273871404113	0 8 80 230 234 264 276 284 420 428 440 470 474 624 696 704	-2596872310008
SPT(16)	3997483253830415777	0 2 24 44 60 84 102 116 120 134 152 176 192 212 234 236	-1616913298344
STPT(10)	3997483826852922611	0 2 6 8 18 20 30 32 36 38	-1043890791510
SPT(16)	3997484108415415339	0 22 54 60 120 144 168 208 234 274 298 322 382 388 420 442	-762328298782
STPT(10)	3997484633727252761	0 2 36 38 78 80 120 122 156 158	-237016461360
SPT(16)	3997484796976647671	0 18 30 38 56 78 128 140 186 198 248 270 288 296 308 326	-73767066450
SPT(16)	3997485075664591169	0 18 32 38 60 110 168 192 200 224 282 332 354 360 374 392	204920877048
STPT(10)	3997485248575954979	0 2 18 20 30 32 42 44 60 62	377832240858
TPT(14)	3997485274691927699	0 2 30 32 48 50 72 74 90 92 132 134 168 170	403948213578
TPT(14)	3997485398620730321	0 2 30 32 90 92 138 140 156 158 186 188 240 242	527877016200
SPT(16)	3997485516868307129	0 2 12 14 180 182 198 200 222 224 240 242 408 410 420 422	646124593008