Prime p₀= 1204780217109629351 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 82 2 34 2 10 2 28 2 40 2 (?)
a_n: 0 2 36 38 120 122 156 158 168 170 198 200 240 242
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: 242
Found by: Megacruncher
db: batch=77, k=14, 34 82 34 10 28 40

SPT(16)	1204779105346002553	0 30 34 64 118 120 190 196 198 204 274 276 330 360 364 394	-1111763626798
STPT(10)	1204779473109087059	0 2 30 32 60 62 90 92 120 122	-744000542292
SPT(16)	1204779532745625253	0 16 36 54 60 96 120 130 180 190 214 250 256 274 294 310	-684364004098
SPT(16)	1204779560540274503	0 14 50 66 78 126 134 170 204 240 248 296 308 324 360 374	-656569354848
STPT(10)	1204779860466202619	0 2 18 20 30 32 42 44 60 62	-356643426732
TPT(14)	1204779996391001141	0 2 60 62 126 128 168 170 180 182 198 200 270 272	-220718628210
SPT(16)	1204780511390556301	0 22 60 78 82 102 120 132 166 178 196 216 220 238 276 298	294280926950
SPT(16)	1204780520205957781	0 60 78 100 120 126 150 210 256 316 340 346 366 388 406 466	303096328430
STPT(10)	1204780598322257417	0 2 24 26 42 44 60 62 84 86	381212628066
SPT(16)	1204780648895900257	0 60 96 100 130 150 154 186 220 252 256 276 306 310 346 406	431786270906
SPT(16)	1204780653534500671	0 6 18 30 46 58 88 100 156 168 198 210 226 238 250 256	436424871320