Prime p₀= 1184363672905318667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 28 2 4 2 172 2 4 2 22 2 (?)
a_n: 0 2 24 26 54 56 60 62 234 236 240 242 264 266
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: 266
Found by: Megacruncher
db: batch=77, k=14, 22 28 4 172 4 22

STPT(10)	1184362979873462507	0 2 24 26 42 44 60 62 84 86	-693031856160
SPT(16)	1184362986218596693	0 28 34 46 48 78 88 144 190 246 256 286 288 300 306 334	-686686721974
STPT(10)	1184363405047545431	0 2 36 38 78 80 120 122 156 158	-267857773236
STPT(10)	1184363411420471507	0 2 30 32 42 44 54 56 84 86	-261484847160
TPT(14)	1184363426520203021	0 2 30 32 138 140 198 200 240 242 306 308 360 362	-246385115646
SPT(16)	1184363511688634107	0 6 22 34 64 90 124 190 306 372 406 432 462 474 490 496	-161216684560
SPT(16)	1184363755942632533	0 14 56 80 90 108 116 156 218 258 266 284 294 318 360 374	83037313866
SPT(16)	1184363882526721903	0 10 28 100 108 114 144 156 208 220 250 256 264 336 354 364	209621403236
TPT(14)	1184364614093487599	0 2 48 50 78 80 168 170 180 182 192 194 210 212	941188168932
STPT(10)	1184364813470702117	0 2 42 44 72 74 102 104 144 146	1140565383450
STPT(10)	1184364899750388467	0 2 42 44 72 74 102 104 144 146	1226845069800