Prime p₀= 2531125140225191009 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 64 2 10 2 16 2 22 2 76 2 (?)
a_n: 0 2 12 14 78 80 90 92 108 110 132 134 210 212
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: 212
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 10 64 10 16 22 76

TPT(14)	2531123849251084187	0 2 84 86 90 92 174 176 270 272 324 326 372 374	-1290974106822
SPT(16)	2531124077987156123	0 8 14 66 80 86 128 170 174 216 258 264 278 330 336 344	-1062238034886
STPT(10)	2531124214931263487	0 2 30 32 42 44 54 56 84 86	-925293927522
SPT(16)	2531124236127980963	0 44 54 68 84 96 114 116 138 140 158 170 186 200 210 254	-904097210046
STPT(10)	2531124756629590727	0 2 12 14 72 74 132 134 144 146	-383595600282
SPT(16)	2531124881083431593	0 8 78 104 108 134 146 156 218 228 240 266 270 296 366 374	-259141759416
SPT(16)	2531125385469811499	0 20 62 74 110 144 150 152 222 224 230 264 300 312 354 374	245244620490
SPT(16)	2531125504852666571	0 2 80 90 128 132 170 182 198 210 248 252 290 300 378 380	364627475562
STPT(10)	2531126079033778559	0 2 48 50 90 92 132 134 180 182	938808587550
TPT(14)	2531126123933342807	0 2 42 44 84 86 102 104 132 134 144 146 222 224	983708151798
SPT(16)	2531126539634012381	0 42 48 110 132 140 152 162 278 288 300 308 330 392 398 440	1399408821372