Prime p₀= 2871400277205079637 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 34 2 10 2 46 2 28 2 10 2 (?)
a_n: 0 2 84 86 120 122 132 134 180 182 210 212 222 224
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: 224
Found by: Landjunge
db: batch=82, k=14, 82 34 10 46 28 10

SPT(16)	2871398383765024637	0 12 32 80 90 110 146 150 182 186 222 242 252 300 320 332	-1893440055000
STPT(10)	2871398559105875801	0 2 30 32 60 62 90 92 120 122	-1718099203836
SPT(16)	2871399102955687963	0 18 106 126 130 136 148 156 220 228 240 246 250 270 358 376	-1174249391674
STPT(10)	2871399165152121389	0 2 30 32 60 62 90 92 120 122	-1112052958248
TPT(14)	2871399604998005351	0 2 18 20 30 32 138 140 186 188 216 218 228 230	-672207074286
SPT(16)	2871399650303430683	0 24 38 48 54 126 134 150 164 180 188 260 266 276 290 314	-626901648954
STPT(10)	2871400331131106441	0 2 6 8 18 20 30 32 36 38	53926026804
STPT(10)	2871400602427429439	0 2 48 50 90 92 132 134 180 182	325222349802
STPT(10)	2871400639667825141	0 2 30 32 60 62 90 92 120 122	362462745504
SPT(16)	2871400664951242733	0 26 44 56 60 66 86 144 206 264 284 290 294 306 324 350	387746163096
SPT(16)	2871400885325994517	0 12 34 72 84 90 96 132 244 280 286 292 304 342 364 376	608120914880