Prime p₀= 2128593563052877409 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 46 2 40 2 16 2 40 2 10 2 (?)
a_n: 0 2 60 62 108 110 150 152 168 170 210 212 222 224
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: 224
Found by: Dirk Broer
db: batch=80, k=14, 58 46 40 16 40 10

SPT(16)	2128591751286395557	0 10 70 100 130 136 154 156 184 186 204 210 240 270 330 340	-1811766481852
STPT(10)	2128592174343472037	0 2 12 14 72 74 132 134 144 146	-1388709405372
SPT(16)	2128592206917793217	0 6 32 54 60 72 90 116 210 236 254 266 272 294 320 326	-1356135084192
TPT(14)	2128592272089315911	0 2 60 62 180 182 216 218 228 230 240 242 258 260	-1290963561498
SPT(16)	2128592299757155381	0 6 10 58 88 90 132 156 172 196 238 240 270 318 322 328	-1263295722028
SPT(16)	2128592781710608123	0 78 120 150 154 186 198 240 304 346 358 390 394 424 466 544	-781342269286
SPT(16)	2128593767319802813	0 10 30 46 60 90 106 120 184 198 214 244 258 274 294 304	204266925404
SPT(16)	2128593792083316413	0 6 20 30 44 84 86 120 140 174 176 216 230 240 254 260	229030439004
STPT(10)	2128594417827459467	0 2 12 14 42 44 72 74 84 86	854774582058
STPT(10)	2128594427737960079	0 2 18 20 30 32 42 44 60 62	864685082670
SPT(16)	2128594509183697043	0 14 54 66 68 74 80 110 114 144 150 156 158 170 210 224	946130819634