Prime p₀= 4506245968498736387 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 112 2 16 2 46 2 112 2 16 2 (?)
a_n: 0 2 30 32 144 146 162 164 210 212 324 326 342 344
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: 344
Found by: Stony666
db: batch=85, k=14, 28 112 16 46 112 16

SPT(16)	4506243959308172947	0 4 12 40 52 66 126 132 214 220 280 294 306 334 342 346	-2009190563440
SPT(16)	4506244537133618047	0 4 54 72 84 112 142 186 220 264 294 322 334 352 402 406	-1431365118340
SPT(16)	4506244612673631041	0 18 162 180 200 218 222 266 282 326 330 348 368 386 530 548	-1355825105346
STPT(10)	4506244732186960907	0 2 60 62 72 74 84 86 144 146	-1236311775480
STPT(10)	4506245206602922379	0 2 42 44 60 62 78 80 120 122	-761895814008
STPT(10)	4506245737451606507	0 2 60 62 72 74 84 86 144 146	-231047129880
STPT(10)	4506246016789801367	0 2 30 32 72 74 114 116 144 146	48291064980
SPT(16)	4506246128822824423	0 30 70 76 90 148 160 168 178 186 198 256 270 276 316 346	160324088036
SPT(16)	4506246162745445497	0 10 30 54 64 120 126 136 324 334 340 396 406 430 450 460	194246709110
SPT(16)	4506246884062731253	0 10 40 54 70 84 94 124 180 210 220 234 250 264 294 304	915563994866
STPT(10)	4506247722420948587	0 2 30 32 72 74 114 116 144 146	1753922212200