Prime p₀= 2726246592924556631 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 154 2 52 2 64 2 82 2 16 2 28 2 (?)
a_n: 0 2 156 158 210 212 276 278 360 362 378 380 408 410
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: 410
Found by: JohnMD
db: batch=82, k=14, 154 52 64 82 16 28

SPT(16)	2726245104668796397	0 60 84 130 180 234 250 264 346 360 376 430 480 526 550 610	-1488255760234
SPT(16)	2726245721990951231	0 32 38 78 102 120 152 158 162 168 200 218 242 282 288 320	-870933605400
SPT(16)	2726245759629677591	0 26 38 92 120 158 168 176 252 260 270 308 336 390 402 428	-833294879040
SPT(16)	2726245926108187591	0 6 12 40 52 108 120 148 210 238 250 306 318 346 352 358	-666816369040
SPT(16)	2726246188475550877	0 10 54 66 70 76 90 232 264 406 420 426 430 442 486 496	-404449005754
SPT(16)	2726246571414964919	0 18 62 74 102 114 140 164 258 282 308 320 348 360 404 422	-21509591712
SPT(16)	2726246698196658929	0 12 32 62 68 74 78 80 162 164 168 174 180 210 230 242	105272102298
STPT(10)	2726247002234222099	0 2 42 44 90 92 138 140 180 182	409309665468
SPT(16)	2726247204054029479	0 18 88 102 124 160 168 180 292 304 312 348 370 384 454 472	611129472848
SPT(16)	2726248423211272417	0 30 54 90 96 120 126 142 174 190 196 220 226 262 286 316	1830286715786
SPT(16)	2726248728398868331	0 18 46 52 58 60 70 96 112 138 148 150 156 162 190 208	2135474311700