Prime p₀= 2268321569755536011 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 70 2 10 2 46 2 178 2 100 2 (?)
a_n: 0 2 6 8 78 80 90 92 138 140 318 320 420 422
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: 422
Found by: Orange Kid
db: batch=81, k=14, 4 70 10 46 178 100

SPT(16)	2268318260997581251	0 18 60 88 106 186 196 198 238 240 250 330 348 376 418 436	-3308757954760
SPT(16)	2268319199223798827	0 54 60 86 120 144 182 204 242 264 302 326 360 386 392 446	-2370531737184
SPT(16)	2268320223767914093	0 18 60 88 126 150 156 178 186 208 214 238 276 304 346 364	-1345987621918
STPT(10)	2268320338433721491	0 2 78 80 108 110 138 140 216 218	-1231321814520
SPT(16)	2268321195830222777	0 2 32 56 66 180 186 192 200 206 212 326 336 360 390 392	-373925313234
SPT(16)	2268321386978113147	0 10 24 46 64 142 196 226 240 270 324 402 420 442 456 466	-182777422864
STPT(10)	2268322565448090119	0 2 42 44 90 92 138 140 180 182	995692554108
STPT(10)	2268322761729385181	0 2 6 8 18 20 30 32 36 38	1191973849170
STPT(10)	2268322851000548861	0 2 30 32 78 80 126 128 156 158	1281245012850
SPT(16)	2268322854410523263	0 20 56 66 78 114 140 198 266 324 350 386 398 408 444 464	1284654987252
SPT(16)	2268322980861730567	0 10 22 34 60 106 112 196 210 294 300 346 372 384 396 406	1411106194556