Prime p₀= 1092569740799960627 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 46 2 46 2 82 2 124 2 70 2 (?)
a_n: 0 2 24 26 72 74 120 122 204 206 330 332 402 404
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: 404
Found by: crashtech
db: batch=76, k=14, 22 46 46 82 124 70

SPT(16)	1092568935800292427	0 22 52 96 102 130 136 180 196 240 246 274 280 324 354 376	-804999668200
STPT(10)	1092569042997829289	0 2 12 14 90 92 168 170 180 182	-697802131338
SPT(16)	1092569233228339543	0 10 36 84 108 120 154 180 244 270 304 316 340 388 414 424	-507571621084
TPT(14)	1092569354472929561	0 2 48 50 60 62 90 92 126 128 138 140 156 158	-386327031066
SPT(16)	1092569531743020827	0 56 72 74 122 126 170 200 276 306 350 354 402 404 420 476	-209056939800
STPT(10)	1092569708536168727	0 2 42 44 72 74 102 104 144 146	-32263791900
TPT(16)	1092569795963581289	0 2 30 32 48 50 72 74 132 134 168 170 180 182 198 200	55163620662
SPT(16)	1092569829724123763	0 24 50 56 96 104 108 134 150 176 180 188 228 234 260 284	88924163136
STPT(10)	1092569863511405087	0 2 30 32 42 44 54 56 84 86	122711444460
SPT(16)	1092570186838368713	0 54 60 80 126 156 170 206 258 294 308 338 384 404 410 464	446038408086
SPT(16)	1092570458421560809	0 10 22 42 78 138 148 202 210 264 274 334 370 390 402 412	717621600182