Prime p₀= 2071181346396047447 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 238 2 82 2 4 2 100 2 16 2 (?)
a_n: 0 2 90 92 330 332 414 416 420 422 522 524 540 542
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: 542
Found by: Cruncher Pete
db: batch=80, k=14, 88 238 82 4 100 16

STPT(10)	2071179658354342097	0 2 42 44 72 74 102 104 144 146	-1688041705350
STPT(10)	2071179699955066817	0 2 30 32 42 44 54 56 84 86	-1646440980630
SPT(16)	2071180107883193873	0 20 54 146 156 174 230 294 296 360 416 434 444 536 570 590	-1238512853574
SPT(16)	2071180397310196999	0 4 22 24 58 82 84 124 168 208 210 234 268 270 288 292	-949085850448
SPT(16)	2071180846691141891	0 12 32 56 140 146 158 216 242 300 312 318 402 426 446 458	-499704905556
SPT(16)	2071181165362461959	0 8 14 30 42 50 60 80 162 182 192 200 212 228 234 242	-181033585488
SPT(16)	2071182186153065597	0 66 96 140 206 264 276 296 300 320 332 390 456 500 530 596	839757018150
SPT(16)	2071182222203126917	0 34 76 84 120 124 126 150 166 190 192 196 232 240 282 316	875807079470
STPT(10)	2071182295696079381	0 2 6 8 48 50 90 92 96 98	949300031934
SPT(16)	2071182344344577141	0 42 60 72 98 126 138 146 192 200 212 240 266 278 296 338	997948529694
SPT(16)	2071182459117002653	0 36 58 76 174 190 214 240 244 270 294 310 408 426 448 484	1112720955206