Prime p₀= 2539466543226536849 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 130 2 124 2 22 2 16 2 46 2 (?)
a_n: 0 2 30 32 162 164 288 290 312 314 330 332 378 380
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: 380
Found by: Penguin
db: batch=82, k=14, 28 130 124 22 16 46

SPT(16)	2539466108423335141	0 12 30 36 46 72 100 112 156 168 196 222 232 238 256 268	-434803201708
TPT(14)	2539466178003358631	0 2 60 62 150 152 198 200 276 278 318 320 360 362	-365223178218
STPT(10)	2539466219162172491	0 2 36 38 78 80 120 122 156 158	-324064364358
SPT(18)	2539466222312187037	0 6 16 34 36 64 70 94 112 114 132 156 162 190 192 210 220 226	-320914349812
SPT(16)	2539466441730587689	0 34 90 102 112 192 202 204 220 222 232 312 322 334 390 424	-101495949160
SPT(16)	2539466519715030259	0 40 78 84 100 102 124 148 204 228 250 252 268 274 312 352	-23511506590
SPT(16)	2539466595749619829	0 30 42 52 72 88 94 124 228 258 264 280 300 310 322 352	52523082980
STPT(10)	2539466807141305799	0 2 18 20 30 32 42 44 60 62	263914768950
STPT(10)	2539466864445482549	0 2 42 44 90 92 138 140 180 182	321218945700
SPT(16)	2539466905512858929	0 2 18 60 90 128 132 152 258 278 282 320 350 392 408 410	362286322080
SPT(16)	2539467319942166087	0 6 14 84 90 104 134 152 174 192 222 236 242 312 320 326	776715629238