Prime p₀= 2729606633090012801 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 106 2 16 2 10 2 70 2 64 2 (?)
a_n: 0 2 30 32 138 140 156 158 168 170 240 242 306 308
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: 308
Found by: herby44
db: batch=82, k=14, 28 106 16 10 70 64

SPT(16)	2729605467862501807	0 10 40 42 52 112 120 144 172 196 204 264 274 276 306 316	-1165227510994
SPT(16)	2729605497715160179	0 22 30 40 70 78 100 108 112 120 142 150 180 190 198 220	-1135374852622
SPT(16)	2729605546300237277	0 12 14 26 72 102 114 180 296 362 374 404 450 462 464 476	-1086789775524
STPT(10)	2729605650412786721	0 2 36 38 78 80 120 122 156 158	-982677226080
TPT(14)	2729605870724872619	0 2 42 44 60 62 132 134 228 230 258 260 342 344	-762365140182
SPT(16)	2729606451492783623	0 38 48 54 116 140 150 168 206 224 234 258 320 326 336 374	-181597229178
SPT(16)	2729606703988957633	0 60 78 120 136 144 150 156 178 184 190 198 214 256 274 334	70898944832
SPT(16)	2729606780876162743	0 34 70 96 154 160 168 216 238 286 294 300 358 384 420 454	147786149942
SPT(16)	2729606840996780011	0 16 22 36 60 82 100 130 138 168 186 208 232 246 252 268	207906767210
SPT(16)	2729607143365247501	0 6 20 26 48 68 72 90 248 266 270 290 312 318 332 338	510275234700
SPT(16)	2729607579648142483	0 16 70 108 190 208 234 240 274 280 306 324 406 444 498 514	946558129682