Prime p₀= 2367891688395886019 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 34 2 10 2 28 2 46 2 (?)
a_n: 0 2 12 14 42 44 78 80 90 92 120 122 168 170
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: 170
Found by: ChUcK
db: batch=81, k=14, 10 28 34 10 28 46

SPT(16)	2367890830137917389	0 54 88 120 138 160 244 250 252 258 342 364 382 414 448 502	-858257968630
SPT(16)	2367891105846783697	0 4 10 22 34 52 60 102 154 196 204 222 234 246 252 256	-582549102322
SPT(16)	2367891239929296409	0 52 54 72 100 142 174 184 318 328 360 402 430 448 450 502	-448466589610
TPT(14)	2367891473601609827	0 2 42 44 54 56 84 86 132 134 144 146 210 212	-214794276192
SPT(16)	2367891591117359927	0 26 36 86 92 114 120 126 140 146 152 174 180 230 240 266	-97278526092
SPT(16)	2367891592767148561	0 78 106 112 210 220 256 280 288 312 348 358 456 462 490 568	-95628737458
STPT(10)	2367891785405093999	0 2 18 20 30 32 42 44 60 62	97009207980
SPT(16)	2367892071022104421	0 12 22 42 46 196 202 208 210 216 222 372 376 396 406 418	382626218402
STPT(10)	2367892197881587841	0 2 36 38 78 80 120 122 156 158	509485701822
STPT(10)	2367892453837945217	0 2 30 32 42 44 54 56 84 86	765442059198
STPT(10)	2367892519562530781	0 2 6 8 18 20 30 32 36 38	831166644762