Prime p₀= 818182306250622431 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 28 2 28 2 22 2 28 2 4 2 (?)
a_n: 0 2 66 68 96 98 126 128 150 152 180 182 186 188
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: 188
Found by: Ralfy
db: batch=73, k=14, 64 28 28 22 28 4

SPT(18)	818181140759955211	0 42 52 66 78 88 96 126 136 222 232 262 270 280 292 306 316 358	-1165490667220
STPT(10)	818181349480281539	0 2 18 20 30 32 42 44 60 62	-956770340892
STPT(10)	818181538375195661	0 2 6 8 18 20 30 32 36 38	-767875426770
STPT(10)	818181714314084171	0 2 6 8 18 20 30 32 36 38	-591936538260
SPT(16)	818181897333911489	0 2 14 44 54 68 92 98 114 120 144 158 168 198 210 212	-408916710942
SPT(16)	818182271792400167	0 2 32 42 86 146 176 186 200 210 240 300 344 354 384 386	-34458222264
STPT(10)	818182374588094457	0 2 30 32 42 44 54 56 84 86	68337472026
SPT(16)	818182491060990323	0 74 80 98 108 116 120 126 158 164 168 176 186 204 210 284	184810367892
SPT(16)	818182881672438991	0 18 22 30 42 70 112 142 156 186 228 256 268 276 280 298	575421816560
STPT(10)	818183020892903759	0 2 42 44 60 62 78 80 120 122	714642281328
SPT(16)	818183150123971949	0 20 78 80 120 140 150 204 218 272 282 302 342 344 402 422	843873349518