Prime p₀= 1568422024110951617 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 10 2 34 2 88 2 40 2 16 2 (?)
a_n: 0 2 12 14 24 26 60 62 150 152 192 194 210 212
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: Theadalus
db: batch=78, k=14, 10 10 34 88 40 16

SPT(16)	1568421135846236681	0 32 38 128 150 162 218 240 260 282 338 350 372 462 468 500	-888264714936
SPT(16)	1568421377005777027	0 4 12 30 40 60 94 112 114 132 166 186 196 214 222 226	-647105174590
SPT(16)	1568421700054619833	0 40 166 168 174 190 196 216 238 258 264 280 286 288 414 454	-324056331784
STPT(10)	1568421700241115491	0 2 30 32 78 80 126 128 156 158	-323869836126
SPT(20)	1568421883042397681	0 6 110 146 156 158 278 336 338 380 396 438 440 498 618 620 630 666 770 776	-141068553936
TPT(14)	1568421997092763529	0 2 12 14 78 80 90 92 138 140 192 194 222 224	-27018188088
SPT(16)	1568422225787272777	0 6 22 36 82 94 120 124 132 136 162 174 220 234 250 256	201676321160
SPT(16)	1568422320595256977	0 12 70 130 184 186 204 232 264 292 310 312 366 426 484 496	296484305360
TPT(14)	1568423394541183679	0 2 42 44 48 50 102 104 252 254 270 272 342 344	1370430232062
STPT(10)	1568423456977950359	0 2 48 50 90 92 132 134 180 182	1432866998742
SPT(16)	1568423527332732923	0 138 140 164 186 210 224 234 350 360 374 398 420 444 446 584	1503221781306