Prime p₀= 2858254739241146951 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 148 2 4 2 88 2 112 2 16 2 (?)
a_n: 0 2 30 32 180 182 186 188 276 278 390 392 408 410
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: Roadranner
db: batch=82, k=14, 28 148 4 88 112 16

STPT(10)	2858253639414969569	0 2 48 50 90 92 132 134 180 182	-1099826177382
SPT(16)	2858253953275708019	0 14 18 44 120 128 168 240 242 314 354 362 438 464 468 482	-785965438932
STPT(10)	2858254375938818807	0 2 30 32 42 44 54 56 84 86	-363302328144
SPT(16)	2858254406578543481	0 26 38 56 66 116 126 138 230 242 252 302 312 330 342 368	-332662603470
STPT(10)	2858254503984325877	0 2 12 14 72 74 132 134 144 146	-235256821074
SPT(16)	2858254514849088701	0 48 66 80 92 98 120 168 170 218 240 246 258 272 290 338	-224392058250
SPT(16)	2858254784528222503	0 28 34 54 88 90 124 138 190 204 238 240 274 294 300 328	45287075552
SPT(16)	2858255199458616653	0 36 48 54 56 98 170 216 218 264 336 378 380 386 398 434	460217469702
TPT(14)	2858255279877068129	0 2 42 44 60 62 78 80 90 92 132 134 210 212	540635921178
STPT(10)	2858255383912797467	0 2 30 32 42 44 54 56 84 86	644671650516
STPT(10)	2858255682912969971	0 2 30 32 78 80 126 128 156 158	943671823020