Prime p₀= 2727581649180472361 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 40 2 130 2 64 2 28 2 10 2 (?)
a_n: 0 2 96 98 138 140 270 272 336 338 366 368 378 380
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: JayPi
db: batch=82, k=14, 94 40 130 64 28 10

SPT(16)	2727580038620863823	0 38 50 66 80 104 108 138 146 176 180 204 218 234 246 284	-1610559608538
SPT(16)	2727580179186876053	0 6 50 54 78 108 120 140 144 164 176 206 230 234 278 284	-1469993596308
STPT(10)	2727580233559034057	0 2 12 14 42 44 72 74 84 86	-1415621438304
STPT(10)	2727580572852848861	0 2 30 32 78 80 126 128 156 158	-1076327623500
SPT(16)	2727581326046111779	0 24 34 48 58 70 112 114 178 180 222 234 244 258 268 292	-323134360582
SPT(16)	2727581456195462561	0 2 18 102 120 140 168 206 252 290 318 338 356 440 456 458	-192985009800
STPT(10)	2727582271228439627	0 2 30 32 72 74 114 116 144 146	622047967266
SPT(16)	2727582416383750969	0 28 30 42 58 72 120 138 154 172 220 234 250 262 264 292	767203278608
SPT(16)	2727582603257170609	0 30 34 58 100 132 142 172 210 240 250 282 324 348 352 382	954076698248
TPT(14)	2727582679862527217	0 2 12 14 24 26 132 134 162 164 174 176 234 236	1030682054856
SPT(16)	2727583144195627789	0 58 112 114 120 154 162 172 180 190 198 232 238 240 294 352	1495015155428