Prime p₀= 2126381766820626647 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 64 2 10 2 46 2 40 2 10 2 (?)
a_n: 0 2 54 56 120 122 132 134 180 182 222 224 234 236
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: 236
Found by: Landjunge
db: batch=80, k=14, 52 64 10 46 40 10

SPT(16)	2126380560663434377	0 24 64 100 136 154 156 210 250 304 306 324 360 396 436 460	-1206157192270
SPT(16)	2126380697692875419	0 38 54 60 68 90 98 120 122 144 152 174 182 188 204 242	-1069127751228
STPT(10)	2126380856180721587	0 2 42 44 72 74 102 104 144 146	-910639905060
SPT(16)	2126381296221391793	0 26 78 104 176 210 216 258 266 308 314 348 420 446 498 524	-470599234854
SPT(16)	2126381521355720171	0 2 36 56 102 156 170 188 210 228 242 296 342 362 396 398	-245464906476
STPT(10)	2126381689093319387	0 2 30 32 72 74 114 116 144 146	-77727307260
STPT(10)	2126382005466593141	0 2 36 38 78 80 120 122 156 158	238645966494
TPT(14)	2126382073225895447	0 2 30 32 132 134 210 212 240 242 252 254 312 314	306405268800
SPT(16)	2126382367316857121	0 2 30 50 62 80 138 156 272 290 348 366 378 398 426 428	600496230474
STPT(10)	2126382372211869389	0 2 48 50 60 62 72 74 120 122	605391242742
STPT(12)	2126382572084797751	0 2 48 50 90 92 126 128 168 170 216 218	805264171104