Prime p₀= 2009276572434158021 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 130 2 370 2 4 2 40 2 28 2 (?)
a_n: 0 2 36 38 168 170 540 542 546 548 588 590 618 620
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: 620
Found by: Landjunge
db: batch=80, k=14, 34 130 370 4 40 28

STPT(10)	2009275455661305191	0 2 6 8 48 50 90 92 96 98	-1116772852830
SPT(16)	2009275637847504869	0 50 62 78 104 120 174 278 324 428 482 498 524 540 552 602	-934586653152
SPT(16)	2009275641031767769	0 34 52 58 72 90 100 118 174 192 202 220 234 240 258 292	-931402390252
SPT(16)	2009276139808481419	0 30 42 58 82 108 124 208 264 348 364 390 414 430 442 472	-432625676602
SPT(16)	2009276443587816401	0 12 32 36 38 50 66 92 126 152 168 180 182 186 206 218	-128846341620
STPT(10)	2009276529857909729	0 2 18 20 30 32 42 44 60 62	-42576248292
SPT(16)	2009276958391019663	0 24 36 54 78 104 150 156 188 194 240 266 290 308 320 344	385956861642
SPT(16)	2009277271324901269	0 18 28 30 42 52 112 142 168 198 258 268 280 282 292 310	698890743248
STPT(10)	2009277546198125051	0 2 36 38 78 80 120 122 156 158	973763967030
STPT(10)	2009277652276003139	0 2 18 20 30 32 42 44 60 62	1079841845118
STPT(12)	2009277755894083061	0 2 78 80 90 92 156 158 168 170 246 248	1183459925040