Prime p₀= 1078795142597509037 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 34 2 28 2 52 2 58 2 106 2 (?)
a_n: 0 2 84 86 120 122 150 152 204 206 264 266 372 374
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: 374
Found by: ginga
db: batch=76, k=14, 82 34 28 52 58 106

TPT(14)	1078793688452884847	0 2 42 44 120 122 132 134 210 212 300 302 330 332	-1454144624190
SPT(16)	1078794250903699867	0 6 42 60 132 144 154 160 186 192 202 214 286 304 340 346	-891693809170
STPT(10)	1078794608259942731	0 2 66 68 108 110 150 152 216 218	-534337566306
SPT(16)	1078794612104040301	0 10 42 138 148 150 162 172 186 196 208 210 220 316 348 358	-530493468736
STPT(10)	1078794686080395797	0 2 60 62 102 104 144 146 204 206	-456517113240
STPT(10)	1078795122701624927	0 2 30 32 42 44 54 56 84 86	-19895884110
STPT(10)	1078795312332990137	0 2 12 14 42 44 72 74 84 86	169735481100
TPT(14)	1078795489513545239	0 2 18 20 42 44 102 104 132 134 168 170 252 254	346916036202
SPT(16)	1078795879142213957	0 20 32 60 110 114 126 174 182 230 242 246 296 324 336 356	736544704920
SPT(16)	1078795981122014773	0 16 24 30 126 144 148 150 154 156 160 178 274 280 288 304	838524505736
STPT(10)	1078796245330468079	0 2 48 50 60 62 72 74 120 122	1102732959042