Prime p₀= 3020969818017633341 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 70 2 28 2 40 2 238 2 34 2 (?)
a_n: 0 2 66 68 138 140 168 170 210 212 450 452 486 488
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: 488
Found by: Alnitak2019
db: batch=82, k=14, 64 70 28 40 238 34

SPT(16)	3020968993164956219	0 24 42 80 152 162 218 248 294 324 380 390 462 500 518 542	-824852677122
TPT(14)	3020969020108927031	0 2 6 8 18 20 60 62 210 212 258 260 336 338	-797908706310
STPT(12)	3020969165813352911	0 2 78 80 108 110 150 152 180 182 258 260	-652204280430
SPT(16)	3020969403044716411	0 16 28 30 70 106 136 148 150 162 192 228 268 270 282 298	-414972916930
SPT(16)	3020969442597668329	0 82 84 144 150 174 180 192 322 334 340 364 370 430 432 514	-375419965012
SPT(16)	3020969535511942033	0 6 10 18 34 48 108 180 244 316 376 390 406 414 418 424	-282505691308
SPT(16)	3020969889933400837	0 4 6 12 46 66 70 172 174 276 280 300 334 340 342 346	71915767496
SPT(16)	3020970152697052991	0 2 26 66 68 80 92 110 138 156 168 180 182 222 246 248	334679419650
STPT(10)	3020970262506934091	0 2 6 8 48 50 90 92 96 98	444489300750
SPT(18)	3020970375958083097	0 24 40 42 94 112 136 156 160 366 370 390 414 432 484 486 502 526	557940449756
TPT(14)	3020970832951251287	0 2 30 32 84 86 120 122 204 206 282 284 324 326	1014933617946