Prime p₀= 2306767923893199407 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 16 2 40 2 40 2 34 2 (?)
a_n: 0 2 12 14 42 44 60 62 102 104 144 146 180 182
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: 182
Found by: vinn@[CNT]
db: batch=81, k=14, 10 28 16 40 40 34

SPT(16)	2306766879602174449	0 12 18 88 108 168 208 220 252 264 304 364 384 454 460 472	-1044291024958
STPT(10)	2306767048588797407	0 2 30 32 42 44 54 56 84 86	-875304402000
SPT(16)	2306767067410044023	0 14 26 54 96 98 158 168 266 276 336 338 380 408 420 434	-856483155384
STPT(10)	2306767195822855061	0 2 6 8 18 20 30 32 36 38	-728070344346
SPT(16)	2306767255597562377	0 42 70 90 144 174 184 214 240 270 280 310 364 384 412 454	-668295637030
SPT(16)	2306767444239676969	0 18 40 82 90 102 108 118 144 154 160 172 180 222 244 262	-479653522438
STPT(10)	2306768108449778627	0 2 90 92 132 134 174 176 264 266	184556579220
SPT(16)	2306768243969911831	0 28 46 88 102 106 118 162 196 240 252 256 270 312 330 358	320076712424
SPT(16)	2306768666734702081	0 10 52 112 126 186 190 226 246 282 286 346 360 420 462 472	742841502674
SPT(16)	2306768669714973587	0 2 30 114 116 140 144 156 170 182 186 210 212 296 324 326	745821774180
STPT(10)	2306768887688742479	0 2 30 32 60 62 90 92 120 122	963795543072