Prime p₀= 1263587300634980471 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 46 2 10 2 76 2 88 2 208 2 (?)
a_n: 0 2 78 80 126 128 138 140 216 218 306 308 516 518
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: 518
Found by: HenkM
db: batch=77, k=14, 76 46 10 76 88 208

SPT(16)	1263585530481377837	0 24 54 156 180 266 294 336 350 392 420 506 530 632 662 686	-1770153602634
SPT(16)	1263585547773401267	0 6 32 44 56 72 74 84 122 132 134 150 162 174 200 206	-1752861579204
SPT(16)	1263585661566698747	0 14 62 84 132 134 170 176 180 186 222 224 272 294 342 356	-1639068281724
STPT(10)	1263585906715511681	0 2 30 32 78 80 126 128 156 158	-1393919468790
SPT(16)	1263587010437495053	0 16 24 36 60 70 94 100 114 120 144 154 178 190 198 214	-290197485418
SPT(16)	1263587213286079777	0 16 36 64 82 120 166 184 222 240 286 324 342 370 390 406	-87348900694
STPT(10)	1263587391809479937	0 2 54 56 72 74 90 92 144 146	91174499466
STPT(10)	1263587690683313417	0 2 90 92 102 104 114 116 204 206	390048332946
TPT(14)	1263587751083350739	0 2 48 50 90 92 138 140 210 212 228 230 252 254	450448370268
SPT(16)	1263588166113056117	0 12 20 36 42 60 80 90 152 162 182 200 206 222 230 242	865478075646
TPT(14)	1263588216040779371	0 2 30 32 66 68 150 152 156 158 198 200 306 308	915405798900