Prime p₀= 1267812968966210201 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 58 2 10 2 16 2 112 2 4 2 (?)
a_n: 0 2 6 8 66 68 78 80 96 98 210 212 216 218
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: 218
Found by: Megacruncher
db: batch=77, k=14, 4 58 10 16 112 4

SPT(16)	1267811792760872267	0 2 42 60 80 84 86 96 200 210 212 216 236 254 294 296	-1176205337934
SPT(16)	1267811843885326451	0 32 56 60 108 110 162 180 188 206 258 260 308 312 336 368	-1125080883750
SPT(16)	1267812248190956033	0 20 26 38 56 66 80 96 140 156 170 180 198 210 216 236	-720775254168
STPT(10)	1267812265745802059	0 2 48 50 90 92 132 134 180 182	-703220408142
SPT(16)	1267812392581396679	0 24 30 42 50 90 108 150 272 314 332 372 380 392 398 422	-576384813522
SPT(16)	1267812707978536327	0 4 10 34 40 76 84 112 114 142 150 186 192 216 222 226	-260987673874
SPT(16)	1267813405624637689	0 24 52 70 82 94 102 138 184 220 228 240 252 270 298 322	436658427488
TPT(14)	1267813455662590931	0 2 120 122 276 278 306 308 318 320 378 380 486 488	486696380730
SPT(16)	1267813985399311993	0 34 40 70 84 108 126 154 240 268 286 310 324 354 360 394	1016433101792
STPT(10)	1267814003740763621	0 2 6 8 18 20 30 32 36 38	1034774553420
SPT(16)	1267814006791990037	0 14 24 50 80 92 266 294 332 360 534 546 576 602 612 626	1037825779836