Prime p₀= 2350319163557629697 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 100 2 34 2 52 2 16 2 (?)
a_n: 0 2 30 32 42 44 144 146 180 182 234 236 252 254
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: 254
Found by: Groo
db: batch=81, k=14, 28 10 100 34 52 16

SPT(16)	2350317597440053711	0 28 40 42 52 88 150 172 186 208 270 306 316 318 330 358	-1566117575986
STPT(10)	2350317669720120809	0 2 18 20 60 62 102 104 120 122	-1493837508888
STPT(10)	2350317885740509427	0 2 12 14 42 44 72 74 84 86	-1277817120270
SPT(16)	2350317909944583497	0 20 44 62 72 80 84 140 174 230 234 242 252 270 294 314	-1253613046200
STPT(10)	2350318015593928481	0 2 78 80 168 170 258 260 336 338	-1147963701216
SPT(16)	2350318129424278019	0 30 44 84 110 128 140 152 240 252 264 282 308 348 362 392	-1034133351678
STPT(10)	2350319719314576407	0 2 30 32 72 74 114 116 144 146	555756946710
SPT(16)	2350319931881044733	0 26 56 60 86 96 120 156 164 200 224 234 260 264 294 320	768323415036
STPT(10)	2350320024345633161	0 2 6 8 48 50 90 92 96 98	860788003464
SPT(16)	2350320068169543049	0 4 72 82 88 112 138 172 180 214 240 264 270 280 348 352	904611913352
SPT(16)	2350320387973779563	0 18 26 60 90 110 116 138 146 168 174 194 224 258 266 284	1224416149866