Prime p₀= 2950505180698953347 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 46 2 28 2 10 2 76 2 22 2 (?)
a_n: 0 2 72 74 120 122 150 152 162 164 240 242 264 266
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: 266
Found by: Landjunge
db: batch=82, k=14, 70 46 28 10 76 22

TPT(16)	2950502726206492139	0 2 60 62 72 74 132 134 210 212 258 260 438 440 462 464	-2454492461208
STPT(10)	2950503619027053359	0 2 48 50 90 92 132 134 180 182	-1561671899988
STPT(10)	2950504172770765439	0 2 12 14 90 92 168 170 180 182	-1007928187908
SPT(16)	2950504305814809089	0 8 12 90 108 114 132 150 152 170 188 194 212 290 294 302	-874884144258
STPT(10)	2950504661132025461	0 2 36 38 78 80 120 122 156 158	-519566927886
SPT(16)	2950505099607292847	0 20 60 90 104 132 152 174 182 204 224 252 266 296 336 356	-81091660500
STPT(10)	2950505451191649047	0 2 30 32 72 74 114 116 144 146	270492695700
STPT(10)	2950506026666801039	0 2 48 50 90 92 132 134 180 182	845967847692
STPT(10)	2950506314610606119	0 2 18 20 30 32 42 44 60 62	1133911652772
SPT(16)	2950506632451416141	0 26 38 110 126 132 168 182 186 200 236 242 258 330 342 368	1451752462794
STPT(10)	2950506833090884097	0 2 30 32 60 62 90 92 120 122	1652391930750