Prime p₀= 1376585608717731911 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 10 2 76 2 40 2 34 2 22 2 (?)
a_n: 0 2 78 80 90 92 168 170 210 212 246 248 270 272
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: 272
Found by: [SG-2W]Kurzer
db: batch=77, k=14, 76 10 76 40 34 22

SPT(16)	1376584787011211039	0 8 12 30 48 98 132 150 152 170 204 254 272 290 294 302	-821706520872
SPT(16)	1376585050195410767	0 60 90 96 152 174 186 216 230 260 272 294 350 356 386 446	-558522321144
STPT(10)	1376585270905755437	0 2 90 92 102 104 114 116 204 206	-337811976474
SPT(16)	1376585373719019643	0 34 46 54 58 76 90 100 114 124 138 156 160 168 180 214	-234998712268
STPT(10)	1376585415434371169	0 2 18 20 30 32 42 44 60 62	-193283360742
STPT(10)	1376585495853166901	0 2 30 32 78 80 126 128 156 158	-112864565010
SPT(18)	1376585674372691317	0 64 120 196 220 234 262 280 316 330 366 384 412 426 450 526 582 646	65654959406
STPT(10)	1376585833558176881	0 2 6 8 48 50 90 92 96 98	224840444970
SPT(16)	1376586020384908757	0 74 84 86 110 120 140 186 194 240 260 270 294 296 306 380	411667176846
SPT(16)	1376586129695589181	0 6 28 52 66 76 78 102 136 160 162 172 186 210 232 238	520977857270
TPT(14)	1376586237453727607	0 2 60 62 102 104 150 152 180 182 222 224 264 266	628735995696