Prime p₀= 2309186957637529727 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 4 2 40 2 28 2 106 2 28 2 (?)
a_n: 0 2 84 86 90 92 132 134 162 164 270 272 300 302
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: 302
Found by: Orange Kid
db: batch=81, k=14, 82 4 40 28 106 28

STPT(10)	2309185992539149979	0 2 12 14 90 92 168 170 180 182	-965098379748
SPT(16)	2309186067542743651	0 12 40 70 82 96 132 160 252 280 316 330 342 372 400 412	-890094786076
SPT(16)	2309186089849567427	0 6 14 32 36 42 126 176 240 290 374 380 384 402 410 416	-867787962300
SPT(16)	2309186537292390499	0 22 58 64 72 144 154 168 214 228 238 310 318 324 360 382	-420345139228
SPT(16)	2309186743039176053	0 14 20 30 44 56 86 144 170 228 258 270 284 294 300 314	-214598353674
SPT(16)	2309186913248190289	0 42 52 118 132 172 174 178 294 298 300 340 354 420 430 472	-44389339438
STPT(10)	2309187087897825659	0 2 18 20 30 32 42 44 60 62	130260295932
STPT(10)	2309187459062522627	0 2 30 32 42 44 54 56 84 86	501424992900
SPT(16)	2309187491956591271	0 6 12 68 72 78 120 132 176 188 230 236 240 296 302 308	534319061544
SPT(16)	2309187760469184011	0 8 36 42 50 92 146 186 212 252 306 348 356 362 390 398	802831654284
STPT(10)	2309188158458029991	0 2 6 8 18 20 30 32 36 38	1200820500264