Prime p₀= 2159691386498650967 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 10 2 136 2 16 2 22 2 (?)
a_n: 0 2 30 32 72 74 84 86 222 224 240 242 264 266
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: 266
Found by: Landjunge
db: batch=81, k=14, 28 40 10 136 16 22

SPT(16)	2159690471348619317	0 50 54 92 120 140 182 210 224 252 294 314 342 380 384 434	-915150031650
STPT(10)	2159690476894182677	0 2 30 32 42 44 54 56 84 86	-909604468290
SPT(16)	2159690524576282081	0 30 40 52 82 112 138 156 262 280 306 336 366 378 388 418	-861922368886
STPT(10)	2159691148671735821	0 2 6 8 18 20 30 32 36 38	-237826915146
SPT(16)	2159691189661321783	0 4 46 84 96 124 148 216 418 486 510 538 550 588 630 634	-196837329184
SPT(16)	2159691360395160871	0 76 102 112 118 138 186 222 256 292 340 360 366 376 402 478	-26103490096
STPT(10)	2159691543336113177	0 2 30 32 42 44 54 56 84 86	156837462210
SPT(16)	2159692356101215171	0 10 36 40 42 60 120 162 220 262 322 340 342 346 372 382	969602564204
TPT(14)	2159692466681974949	0 2 48 50 72 74 90 92 138 140 168 170 180 182	1080183323982
SPT(16)	2159692859413902497	0 6 12 26 44 104 144 152 174 182 222 282 300 314 320 326	1472915251530
STPT(10)	2159693361421486997	0 2 12 14 42 44 72 74 84 86	1974922836030