Prime p₀= 3006499572908224397 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 58 2 58 2 76 2 40 2 4 2 (?)
a_n: 0 2 54 56 114 116 174 176 252 254 294 296 300 302
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: 302
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 52 58 58 76 40 4

SPT(16)	3006498498461883091	0 88 118 132 142 148 162 168 190 196 210 216 226 240 270 358	-1074446341306
STPT(10)	3006498683083693937	0 2 60 62 72 74 84 86 144 146	-889824530460
TPT(14)	3006498705826834079	0 2 30 32 42 44 180 182 222 224 252 254 330 332	-867081390318
STPT(10)	3006498926813485721	0 2 36 38 78 80 120 122 156 158	-646094738676
SPT(16)	3006499106243093347	0 24 34 52 66 94 96 112 144 160 162 190 204 222 232 256	-466665131050
SPT(16)	3006499423076508479	0 2 8 38 60 68 74 84 278 288 294 302 324 354 360 362	-149831715918
STPT(10)	3006500166388585481	0 2 156 158 168 170 180 182 336 338	593480361084
SPT(16)	3006500634265240709	0 2 24 62 104 150 210 240 284 314 374 420 462 500 522 524	1061357016312
SPT(16)	3006500851305031651	0 42 46 82 126 130 148 190 228 270 288 292 336 372 376 418	1278396807254
STPT(10)	3006500933801535251	0 2 6 8 48 50 90 92 96 98	1360893310854
SPT(16)	3006501115983244861	0 16 48 70 108 126 160 168 178 186 220 238 276 298 330 346	1543075020464