Prime p₀= 2050102092953274629 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 316 2 40 2 70 2 28 2 64 2 58 2 (?)
a_n: 0 2 318 320 360 362 432 434 462 464 528 530 588 590
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: 590
Found by: Landjunge
db: batch=80, k=14, 316 40 70 28 64 58

SPT(16)	2050100012559727649	0 44 50 54 78 104 110 138 170 198 204 230 254 258 264 308	-2080393546980
SPT(16)	2050100904309495127	0 12 96 124 132 142 160 210 226 276 294 304 312 340 424 436	-1188643779502
SPT(16)	2050101654180697847	0 14 44 86 114 162 174 182 204 212 224 272 300 342 372 386	-438772576782
SPT(16)	2050101748890562561	0 6 36 42 88 108 112 132 166 186 190 210 256 262 292 298	-344062712068
STPT(10)	2050101836557778291	0 2 36 38 78 80 120 122 156 158	-256395496338
STPT(10)	2050101944474997377	0 2 30 32 42 44 54 56 84 86	-148478277252
SPT(16)	2050102317384685793	0 8 20 50 54 60 78 140 144 206 224 230 234 264 276 284	224431411164
STPT(10)	2050102586592419501	0 2 6 8 18 20 30 32 36 38	493639144872
STPT(10)	2050102745799270101	0 2 36 38 78 80 120 122 156 158	652845995472
SPT(16)	2050102845019379851	0 18 42 70 88 112 130 178 240 288 306 330 348 376 400 418	752066105222
SPT(20)	2050102990380105677	0 20 30 44 60 74 90 156 176 186 230 240 260 326 342 356 372 386 396 416	897426831048