Prime p₀= 954218952964577687 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 70 2 70 2 4 2 58 2 (?)
a_n: 0 2 30 32 60 62 132 134 204 206 210 212 270 272
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: 272
Found by: Theadalus
db: batch=76, k=14, 28 28 70 70 4 58

SPT(16)	954218127564422689	0 12 40 52 78 148 150 168 244 262 264 334 360 372 400 412	-825400154998
SPT(16)	954218350046227991	0 18 30 92 102 140 168 180 260 272 300 338 348 410 422 440	-602918349696
SPT(16)	954218629033902857	0 30 60 72 132 162 164 170 204 210 212 242 302 314 344 374	-323930674830
TPT(14)	954218651387790029	0 2 180 182 192 194 222 224 348 350 360 362 378 380	-301576787658
SPT(16)	954218841604634663	0 26 30 36 50 56 66 78 158 170 180 186 200 206 210 236	-111359943024
STPT(10)	954218926593073187	0 2 12 14 72 74 132 134 144 146	-26371504500
STPT(10)	954219061220952521	0 2 36 38 78 80 120 122 156 158	108256374834
TPT(14)	954219624303997937	0 2 30 32 54 56 84 86 174 176 222 224 264 266	671339420250
SPT(16)	954220233451414109	0 12 92 108 120 138 152 180 230 258 272 290 302 318 398 410	1280486836422
SPT(16)	954220466713499927	0 14 126 146 156 170 174 204 236 266 270 284 294 314 426 440	1513748922240
STPT(10)	954220907913491459	0 2 42 44 90 92 138 140 180 182	1954948913772