Prime p₀= 2531126123933342807 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 40 2 16 2 28 2 10 2 76 2 (?)
a_n: 0 2 42 44 84 86 102 104 132 134 144 146 222 224
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: 224
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 40 40 16 28 10 76

STPT(10)	2531124756629590727	0 2 12 14 72 74 132 134 144 146	-1367303752080
SPT(16)	2531124881083431593	0 8 78 104 108 134 146 156 218 228 240 266 270 296 366 374	-1242849911214
TPT(14)	2531125140225191009	0 2 12 14 78 80 90 92 108 110 132 134 210 212	-983708151798
SPT(16)	2531125385469811499	0 20 62 74 110 144 150 152 222 224 230 264 300 312 354 374	-738463531308
SPT(16)	2531125504852666571	0 2 80 90 128 132 170 182 198 210 248 252 290 300 378 380	-619080676236
STPT(10)	2531126079033778559	0 2 48 50 90 92 132 134 180 182	-44899564248
SPT(16)	2531126539634012381	0 42 48 110 132 140 152 162 278 288 300 308 330 392 398 440	415700669574
STPT(10)	2531126785092126581	0 2 6 8 48 50 90 92 96 98	661158783774
SPT(16)	2531126790076309577	0 14 20 62 80 84 150 152 162 164 230 234 252 294 300 314	666142966770
STPT(10)	2531126924612085221	0 2 30 32 120 122 210 212 240 242	800678742414
SPT(16)	2531127151676136779	0 38 98 104 108 122 132 134 138 140 150 164 168 174 234 272	1027742793972