Prime p₀= 1314087610155946361 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 112 2 88 2 4 2 58 2 70 2 (?)
a_n: 0 2 36 38 150 152 240 242 246 248 306 308 378 380
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: 380
Found by: Theadalus
db: batch=77, k=14, 34 112 88 4 58 70

SPT(16)	1314086386378635977	0 2 24 56 104 144 162 186 230 254 272 312 360 392 414 416	-1223777310384
STPT(10)	1314086608519673249	0 2 18 20 30 32 42 44 60 62	-1001636273112
SPT(16)	1314086870114273789	0 2 30 72 80 84 114 140 174 200 230 234 242 284 312 314	-740041672572
SPT(16)	1314086895249367879	0 54 72 100 124 178 204 220 222 238 264 318 342 370 388 442	-714906578482
STPT(10)	1314087067836952229	0 2 42 44 60 62 78 80 120 122	-542318994132
SPT(16)	1314087481714773637	0 34 54 72 76 106 166 202 204 240 300 330 334 352 372 406	-128441172724
SPT(16)	1314087665976398641	0 42 70 76 82 126 132 172 210 250 256 300 306 312 340 382	55820452280
SPT(16)	1314087765634391963	0 8 20 36 66 78 80 98 186 204 206 218 248 264 276 284	155478445602
STPT(10)	1314087766258584671	0 2 6 8 48 50 90 92 96 98	156102638310
SPT(16)	1314087889759300939	0 34 40 70 82 84 90 114 178 202 208 210 222 252 258 292	279603354578
SPT(16)	1314087890874071711	0 66 68 90 102 116 146 158 180 192 222 236 248 270 272 338	280718125350