Prime p₀= 869006447996674121 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 16 2 22 2 16 2 16 2 10 2 (?)
a_n: 0 2 78 80 96 98 120 122 138 140 156 158 168 170
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: 170
Found by: Coleslaw
db: batch=73, k=14, 76 16 22 16 16 10

SPT(16)	869005269492233903	0 50 54 80 96 144 204 234 380 410 470 518 534 560 564 614	-1178504440218
STPT(10)	869005396805762297	0 2 54 56 72 74 90 92 144 146	-1051190911824
STPT(10)	869005715015462417	0 2 30 32 42 44 54 56 84 86	-732981211704
STPT(10)	869005808104607651	0 2 30 32 78 80 126 128 156 158	-639892066470
STPT(10)	869005950186585647	0 2 42 44 72 74 102 104 144 146	-497810088474
STPT(10)	869006277190138181	0 2 6 8 48 50 90 92 96 98	-170806535940
STPT(10)	869006652120589427	0 2 30 32 42 44 54 56 84 86	204123915306
SPT(16)	869006891438938853	0 18 54 96 98 110 128 138 326 336 354 366 368 410 446 464	443442264732
SPT(16)	869006937093984817	0 22 42 64 72 126 144 156 160 172 190 244 252 274 294 316	489097310696
STPT(10)	869006964062501021	0 2 6 8 18 20 30 32 36 38	516065826900
SPT(16)	869007111834896611	0 12 30 40 48 52 58 70 78 90 96 100 108 118 136 148	663838222490