Prime p₀= 2709108629813489999 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 4 2 22 2 88 2 4 2 28 2 (?)
a_n: 0 2 12 14 18 20 42 44 132 134 138 140 168 170
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: 170
Found by: JayPi
db: batch=82, k=14, 10 4 22 88 4 28

SPT(16)	2709106305112423123	0 40 64 66 90 178 196 204 220 228 246 334 358 360 384 424	-2324701066876
SPT(16)	2709107049517803769	0 24 28 48 90 150 154 174 178 198 202 262 304 324 328 352	-1580295686230
SPT(16)	2709107053080561901	0 6 10 42 82 118 130 172 216 258 270 306 346 378 382 388	-1576732928098
STPT(10)	2709107070778527227	0 2 54 56 72 74 90 92 144 146	-1559034962772
TPT(14)	2709107493347863469	0 2 30 32 78 80 162 164 168 170 180 182 198 200	-1136465626530
STPT(10)	2709108384059241917	0 2 30 32 42 44 54 56 84 86	-245754248082
SPT(16)	2709108922354548361	0 42 72 126 130 156 186 208 300 322 352 378 382 436 466 508	292541058362
SPT(16)	2709109217853212431	0 10 48 66 102 130 166 180 208 222 258 286 322 340 378 388	588039722432
STPT(10)	2709109542038652017	0 2 42 44 72 74 102 104 144 146	912225162018
SPT(16)	2709109552732851179	0 14 18 74 80 104 108 170 228 290 294 318 324 380 384 398	922919361180
STPT(10)	2709109587481994699	0 2 30 32 60 62 90 92 120 122	957668504700