Prime p₀= 868127684029898141 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 10 2 70 2 106 2 28 2 16 2 (?)
a_n: 0 2 66 68 78 80 150 152 258 260 288 290 306 308
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: 308
Found by: [AF>EDLS] GGTF
db: batch=73, k=14, 64 10 70 106 28 16

STPT(12)	868127244004972337	0 2 42 44 72 74 150 152 180 182 222 224	-440024925804
TPT(14)	868127270681168879	0 2 108 110 138 140 168 170 252 254 390 392 402 404	-413348729262
SPT(13)	868127446538701253	0 6 24 36 90 114 120 126 150 204 216 234 240	-237491196888
SPT(16)	868127481856692143	0 8 56 116 120 140 146 170 204 228 234 254 258 318 366 374	-202173205998
SPT(16)	868127501847296039	0 18 32 48 72 108 150 188 192 230 272 308 332 348 362 380	-182182602102
STPT(10)	868127660208726059	0 2 18 20 30 32 42 44 60 62	-23821172082
SPT(16)	868127754835309123	0 46 70 78 100 126 148 168 226 246 268 294 316 324 348 394	70805410982
STPT(10)	868128334580424821	0 2 36 38 78 80 120 122 156 158	650550526680
SPT(16)	868128348029342249	0 20 50 54 80 104 128 150 152 174 198 222 248 252 282 302	663999444108
STPT(10)	868128367107989147	0 2 30 32 42 44 54 56 84 86	683078091006
TPT(14)	868128599030745881	0 2 6 8 78 80 90 92 96 98 108 110 138 140	915000847740