Prime p₀= 1288758497999699579 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 148 2 4 2 10 2 28 2 76 2 (?)
a_n: 0 2 72 74 222 224 228 230 240 242 270 272 348 350
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: 350
Found by: HenkM
db: batch=77, k=14, 70 148 4 10 28 76

SPT(16)	1288757621191695461	0 30 48 56 60 72 86 122 126 162 176 188 192 200 218 248	-876808004118
STPT(10)	1288757712971406911	0 2 36 38 78 80 120 122 156 158	-785028292668
TPT(16)	1288758181211614031	0 2 18 20 120 122 156 158 198 200 240 242 378 380 396 398	-316788085548
STPT(10)	1288758206156928509	0 2 30 32 60 62 90 92 120 122	-291842771070
STPT(10)	1288758361766420099	0 2 42 44 60 62 78 80 120 122	-136233279480
STPT(10)	1288758376014923477	0 2 42 44 72 74 102 104 144 146	-121984776102
SPT(16)	1288758611693714779	0 22 24 52 88 94 102 148 234 280 288 294 330 358 360 382	113694015200
STPT(10)	1288758985303542617	0 2 42 44 72 74 102 104 144 146	487303843038
STPT(10)	1288758987767758889	0 2 48 50 90 92 132 134 180 182	489768059310
SPT(16)	1288759043123494961	0 6 30 36 42 50 56 68 240 252 258 266 272 278 302 308	545123795382
TPT(14)	1288759406279776181	0 2 36 38 78 80 126 128 156 158 168 170 258 260	908280076602