Prime p₀= 996820580848366661 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 178 2 10 2 64 2 28 2 28 2 (?)
a_n: 0 2 78 80 258 260 270 272 336 338 366 368 396 398
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: 398
Found by: Theadalus
db: batch=76, k=14, 76 178 10 64 28 28

SPT(16)	996817939997908447	0 4 6 42 46 52 82 90 136 144 174 180 184 220 222 226	-2640850458214
STPT(10)	996818415965037737	0 2 30 32 42 44 54 56 84 86	-2164883328924
STPT(10)	996818458464132149	0 2 18 20 30 32 42 44 60 62	-2122384234512
STPT(10)	996818776708670471	0 2 6 8 48 50 90 92 96 98	-1804139696190
SPT(16)	996819435669842287	0 6 10 46 66 70 72 90 112 130 132 136 156 192 196 202	-1145178524374
SPT(16)	996819766271182981	0 12 28 40 58 78 100 102 106 108 130 150 168 180 196 208	-814577183680
STPT(10)	996820731350461019	0 2 30 32 60 62 90 92 120 122	150502094358
STPT(10)	996821088549143831	0 2 30 32 120 122 210 212 240 242	507700777170
SPT(13)	996821113973404121	0 30 72 78 90 108 120 132 150 162 168 210 240	533125037460
SPT(16)	996821537069694569	0 48 60 132 140 158 164 168 224 228 234 252 260 332 344 392	956221327908
STPT(10)	996821856178203899	0 2 18 20 30 32 42 44 60 62	1275329837238