Prime p₀= 2164269582395375627 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 40 2 46 2 76 2 130 2 (?)
a_n: 0 2 30 32 42 44 84 86 132 134 210 212 342 344
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: 344
Found by: Landjunge
db: batch=81, k=14, 28 10 40 46 76 130

SPT(16)	2164268279922231289	0 42 48 58 72 78 88 114 118 144 154 160 174 184 190 232	-1302473144338
STPT(10)	2164268547769268777	0 2 42 44 72 74 102 104 144 146	-1034626106850
TPT(14)	2164268690909061461	0 2 6 8 96 98 156 158 168 170 180 182 228 230	-891486314166
SPT(16)	2164268753917644349	0 10 54 94 100 120 174 178 180 184 238 258 264 304 348 358	-828477731278
SPT(16)	2164269353158282541	0 6 8 26 36 48 162 300 308 446 560 572 582 600 602 608	-229237093086
TPT(14)	2164269497600943581	0 2 6 8 120 122 156 158 258 260 288 290 300 302	-84794432046
SPT(16)	2164269725906995087	0 12 66 76 82 96 150 156 160 166 220 234 240 250 304 316	143511619460
STPT(10)	2164269765768340331	0 2 6 8 48 50 90 92 96 98	183372964704
STPT(10)	2164270205398310897	0 2 30 32 42 44 54 56 84 86	623002935270
SPT(16)	2164270458555523249	0 12 24 70 148 172 180 210 232 262 270 294 372 418 430 442	876160147622
TPT(14)	2164270858563553721	0 2 18 20 78 80 90 92 120 122 198 200 210 212	1276168178094