Prime p₀= 3006498705826834079 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 136 2 40 2 28 2 76 2 (?)
a_n: 0 2 30 32 42 44 180 182 222 224 252 254 330 332
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: 332
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 28 10 136 40 28 76

SPT(16)	3006498190214267657	0 20 44 60 102 116 152 254 282 384 420 434 476 492 516 536	-515612566422
STPT(10)	3006498221242282967	0 2 30 32 72 74 114 116 144 146	-484584551112
SPT(16)	3006498331973178967	0 64 70 82 96 100 124 150 196 222 246 250 264 276 282 346	-373853655112
SPT(16)	3006498389471503781	0 18 38 110 140 150 200 218 270 288 338 348 378 450 470 488	-316355330298
SPT(16)	3006498498461883091	0 88 118 132 142 148 162 168 190 196 210 216 226 240 270 358	-207364950988
STPT(10)	3006498683083693937	0 2 60 62 72 74 84 86 144 146	-22743140142
STPT(10)	3006498926813485721	0 2 36 38 78 80 120 122 156 158	220986651642
SPT(16)	3006499106243093347	0 24 34 52 66 94 96 112 144 160 162 190 204 222 232 256	400416259268
SPT(16)	3006499423076508479	0 2 8 38 60 68 74 84 278 288 294 302 324 354 360 362	717249674400
TPT(14)	3006499572908224397	0 2 54 56 114 116 174 176 252 254 294 296 300 302	867081390318
STPT(10)	3006500166388585481	0 2 156 158 168 170 180 182 336 338	1460561751402