Prime p₀= 1286574810570014729 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 118 2 40 2 46 2 10 2 64 2 (?)
a_n: 0 2 30 32 150 152 192 194 240 242 252 254 318 320
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: 320
Found by: Cruncher Pete
db: batch=77, k=14, 28 118 40 46 10 64

SPT(16)	1286573454956213471	0 56 108 110 126 146 152 182 186 216 222 242 258 260 312 368	-1355613801258
STPT(10)	1286573481803064779	0 2 18 20 30 32 42 44 60 62	-1328766949950
SPT(16)	1286573542913100269	0 18 32 48 72 114 132 144 158 170 188 230 254 270 284 302	-1267656914460
STPT(10)	1286573582673180029	0 2 48 50 90 92 132 134 180 182	-1227896834700
SPT(18)	1286573641929758569	0 4 34 48 60 114 118 132 142 270 280 294 298 352 364 378 408 412	-1168640256160
SPT(16)	1286574088213837909	0 10 40 54 72 84 100 124 168 192 208 220 238 252 282 292	-722356176820
SPT(16)	1286574876901870217	0 2 26 30 72 102 134 140 156 162 194 224 266 270 294 296	66331855488
STPT(10)	1286574893898076631	0 2 30 32 60 62 90 92 120 122	83328061902
SPT(16)	1286574917885254871	0 2 26 42 102 126 152 186 206 240 266 290 350 366 390 392	107315240142
SPT(16)	1286574968186168939	0 20 78 98 102 132 252 270 290 308 428 458 462 482 540 560	157616154210
SPT(16)	1286575111642572839	0 48 68 80 90 92 98 132 140 174 180 182 192 204 224 272	301072558110