Prime p₀= 2531123849251084187 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 4 2 82 2 94 2 52 2 46 2 (?)
a_n: 0 2 84 86 90 92 174 176 270 272 324 326 372 374
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: 374
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 82 4 82 94 52 46

STPT(10)	2531122614349976159	0 2 42 44 60 62 78 80 120 122	-1234901108028
SPT(16)	2531123158370837083	0 34 70 96 160 204 216 238 426 448 460 504 568 594 630 664	-690880247104
STPT(10)	2531123351475898589	0 2 12 14 90 92 168 170 180 182	-497775185598
SPT(16)	2531123459672299553	0 20 50 66 68 158 176 188 306 318 336 426 428 444 474 494	-389578784634
STPT(10)	2531123601379051037	0 2 60 62 102 104 144 146 204 206	-247872033150
SPT(16)	2531123747452828859	0 8 38 48 50 62 80 140 210 270 288 300 302 312 342 350	-101798255328
SPT(16)	2531124077987156123	0 8 14 66 80 86 128 170 174 216 258 264 278 330 336 344	228736071936
STPT(10)	2531124214931263487	0 2 30 32 42 44 54 56 84 86	365680179300
SPT(16)	2531124236127980963	0 44 54 68 84 96 114 116 138 140 158 170 186 200 210 254	386876896776
STPT(10)	2531124756629590727	0 2 12 14 72 74 132 134 144 146	907378506540
SPT(16)	2531124881083431593	0 8 78 104 108 134 146 156 218 228 240 266 270 296 366 374	1031832347406