Prime p₀= 3007718640727898369 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 76 2 40 2 4 2 28 2 10 2 (?)
a_n: 0 2 72 74 150 152 192 194 198 200 228 230 240 242
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: 242
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 70 76 40 4 28 10

STPT(10)	3007716947319423011	0 2 30 32 78 80 126 128 156 158	-1693408475358
STPT(10)	3007717137327194177	0 2 30 32 42 44 54 56 84 86	-1503400704192
STPT(10)	3007717217326774607	0 2 30 32 72 74 114 116 144 146	-1423401123762
STPT(10)	3007717477881304997	0 2 12 14 72 74 132 134 144 146	-1162846593372
SPT(16)	3007717564835546951	0 6 56 86 90 138 146 170 216 240 248 296 300 330 380 386	-1075892351418
STPT(10)	3007717653614009459	0 2 12 14 90 92 168 170 180 182	-987113888910
SPT(16)	3007718942058594077	0 12 56 84 140 152 164 182 234 252 264 276 332 360 404 416	301330695708
SPT(16)	3007718992651375817	0 42 62 80 126 140 146 192 194 240 246 260 306 324 344 386	351923477448
SPT(16)	3007719435939342823	0 40 66 70 186 256 264 298 306 340 348 418 534 538 564 604	795211444454
TPT(16)	3007719629878900679	0 2 30 32 42 44 72 74 120 122 150 152 318 320 330 332	989151002310
STPT(10)	3007720134201350387	0 2 30 32 42 44 54 56 84 86	1493473452018