Prime p₀= 2313453023622150071 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 46 2 40 2 40 2 4 2 (?)
a_n: 0 2 30 32 48 50 96 98 138 140 180 182 186 188
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: 188
Found by: Landjunge
db: batch=81, k=14, 28 16 46 40 40 4

SPT(16)	2313451943237309009	0 18 38 48 92 132 150 158 192 200 218 258 302 312 332 350	-1080384841062
STPT(10)	2313451987052273057	0 2 12 14 42 44 72 74 84 86	-1036569877014
SPT(16)	2313452395805030069	0 38 74 98 144 150 174 218 240 284 308 314 360 384 420 458	-627817120002
STPT(10)	2313452503355772137	0 2 60 62 72 74 84 86 144 146	-520266377934
SPT(16)	2313452714778876859	0 4 52 60 70 112 130 154 198 222 240 282 292 300 348 352	-308843273212
SPT(16)	2313452855060176169	0 14 18 44 74 90 104 120 278 294 308 324 354 380 384 398	-168561973902
SPT(16)	2313453154365186173	0 14 20 48 54 90 120 138 176 194 224 260 266 294 300 314	130743036102
SPT(16)	2313453297520286393	0 20 44 90 98 110 170 194 240 264 324 336 344 390 414 434	273898136322
SPT(16)	2313453439950162193	0 36 90 150 210 216 234 258 376 400 418 424 484 544 598 634	416328012122
STPT(10)	2313453440634171887	0 2 30 32 102 104 174 176 204 206	417012021816
STPT(10)	2313453473486993729	0 2 48 50 90 92 132 134 180 182	449864843658