Prime p₀= 2727129473149302587 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 112 2 4 2 22 2 166 2 10 2 28 2 (?)
a_n: 0 2 114 116 120 122 144 146 312 314 324 326 354 356
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: 356
Found by: JayPi
db: batch=82, k=14, 112 4 22 166 10 28

STPT(10)	2727127727390127167	0 2 30 32 42 44 54 56 84 86	-1745759175420
SPT(16)	2727128001938759843	0 84 134 140 210 254 260 270 284 294 300 344 414 420 470 554	-1471210542744
SPT(16)	2727128245056929029	0 18 64 70 78 84 138 142 150 154 208 214 222 228 274 292	-1228092373558
SPT(16)	2727128544485559241	0 40 46 58 60 88 112 118 150 156 180 208 210 222 228 268	-928663743346
SPT(16)	2727128936899019557	0 6 36 66 142 144 156 204 352 400 412 414 490 520 550 556	-536250283030
SPT(16)	2727129326206993847	0 12 44 80 96 104 140 144 152 156 192 200 216 252 284 296	-146942308740
SPT(16)	2727129481270614041	0 20 48 62 96 98 110 152 186 228 240 242 276 290 318 338	8121311454
STPT(10)	2727129677731993691	0 2 66 68 108 110 150 152 216 218	204582691104
SPT(16)	2727129678979117079	0 38 42 62 98 104 128 140 162 174 198 204 240 260 264 302	205829814492
SPT(16)	2727129965413571087	0 30 44 62 96 102 110 132 164 186 194 200 234 252 266 296	492264268500
STPT(10)	2727130370719163597	0 2 24 26 42 44 60 62 84 86	897569861010