Prime p₀= 2734951489167011129 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 160 2 4 2 28 2 40 2 10 2 76 2 (?)
a_n: 0 2 162 164 168 170 198 200 240 242 252 254 330 332
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: 332
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 160 4 28 40 10 76

TPT(14)	2734950822941867681	0 2 90 92 138 140 216 218 336 338 348 350 426 428	-666225143448
STPT(10)	2734950970893477701	0 2 66 68 138 140 210 212 276 278	-518273533428
SPT(18)	2734950990217723379	0 32 42 104 110 168 182 188 222 230 264 270 284 342 348 410 420 452	-498949287750
SPT(16)	2734951174720815187	0 12 30 34 40 70 76 114 172 210 216 246 252 256 274 286	-314446195942
SPT(16)	2734951192508829953	0 50 60 74 116 120 156 176 228 248 284 288 330 344 354 404	-296658181176
STPT(10)	2734951274414269019	0 2 48 50 90 92 132 134 180 182	-214752742110
SPT(16)	2734952095551501191	0 98 120 132 170 188 218 248 252 282 312 330 368 380 402 500	606384490062
TPT(14)	2734952179462454561	0 2 120 122 276 278 318 320 330 332 348 350 366 368	690295443432
SPT(16)	2734952259063986707	0 4 16 72 76 100 114 142 144 172 186 210 214 270 282 286	769896975578
STPT(10)	2734952484050942567	0 2 24 26 42 44 60 62 84 86	994883931438
SPT(16)	2734952488593149813	0 20 24 50 60 66 104 126 164 186 224 230 240 266 270 290	999426138684