Prime p₀= 2596431161298340997 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 202 2 16 2 10 2 16 2 40 2 76 2 (?)
a_n: 0 2 204 206 222 224 234 236 252 254 294 296 372 374
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: 374
Found by: JayPi
db: batch=82, k=14, 202 16 10 16 40 76

SPT(16)	2596429333245765461	0 30 36 48 66 72 78 80 138 140 146 152 170 182 188 218	-1828052575536
STPT(10)	2596429442851521647	0 2 30 32 42 44 54 56 84 86	-1718446819350
STPT(10)	2596429549569103067	0 2 30 32 120 122 210 212 240 242	-1611729237930
STPT(10)	2596430026084488017	0 2 54 56 72 74 90 92 144 146	-1135213852980
STPT(10)	2596430169443726849	0 2 48 50 60 62 72 74 120 122	-991854614148
SPT(16)	2596430269094005411	0 46 48 88 106 112 130 156 172 198 216 222 240 280 282 328	-892204335586
SPT(16)	2596431276819555541	0 28 72 100 112 120 130 142 156 168 178 186 198 226 270 298	115521214544
SPT(16)	2596431857177082227	0 30 66 72 84 86 92 140 186 234 240 242 254 260 296 326	695878741230
SPT(16)	2596432066748125877	0 84 102 146 150 216 242 264 272 294 320 386 390 434 452 536	905449784880
STPT(10)	2596432376420647949	0 2 18 20 30 32 42 44 60 62	1215122306952
STPT(10)	2596432581176041637	0 2 30 32 42 44 54 56 84 86	1419877700640