Prime p₀= 2167130262516112601 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 112 2 16 2 10 2 34 2 28 2 (?)
a_n: 0 2 66 68 180 182 198 200 210 212 246 248 276 278
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: 278
Found by: ginga
db: batch=81, k=14, 64 112 16 10 34 28

SPT(16)	2167129430898264901	0 22 28 60 70 90 96 102 106 112 118 138 148 180 186 208	-831617847700
STPT(10)	2167129499694882377	0 2 30 32 72 74 114 116 144 146	-762821230224
STPT(10)	2167129593399096407	0 2 12 14 72 74 132 134 144 146	-669117016194
SPT(16)	2167129836928428557	0 26 54 92 120 150 182 264 302 384 416 446 474 512 540 566	-425587684044
STPT(10)	2167129837007919149	0 2 42 44 60 62 78 80 120 122	-425508193452
SPT(16)	2167130063695105051	0 28 72 96 118 142 160 196 252 288 306 330 352 376 420 448	-198821007550
STPT(12)	2167130463876388607	0 2 42 44 60 62 114 116 132 134 174 176	201360276006
SPT(16)	2167131368138722873	0 18 70 76 108 144 154 174 220 240 250 286 318 324 376 394	1105622610272
STPT(10)	2167132244020241087	0 2 42 44 72 74 102 104 144 146	1981504128486
SPT(16)	2167132344427641653	0 30 38 98 138 144 210 230 234 254 320 326 366 426 434 464	2081911529052
SPT(16)	2167132442137238717	0 14 32 42 102 140 164 180 224 240 264 302 362 372 390 404	2179621126116