Prime p₀= 921768718959743537 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 106 2 136 2 82 2 28 2 4 2 (?)
a_n: 0 2 84 86 192 194 330 332 414 416 444 446 450 452
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: 452
Found by: ginga
db: batch=76, k=14, 82 106 136 82 28 4

SPT(16)	921768292746365761	0 30 48 100 130 132 138 142 198 202 208 210 240 292 310 340	-426213377776
SPT(16)	921768371838833611	0 28 70 78 82 88 112 130 138 156 180 186 190 198 240 268	-347120909926
SPT(16)	921768504837114523	0 28 30 58 96 136 166 198 208 240 270 310 348 376 378 406	-214122629014
STPT(10)	921768520546612757	0 2 42 44 72 74 102 104 144 146	-198413130780
SPT(16)	921768593858343923	0 20 26 54 60 68 104 128 156 180 216 224 230 258 264 284	-125101399614
STPT(10)	921768668719515341	0 2 6 8 48 50 90 92 96 98	-50240228196
STPT(10)	921768769423563167	0 2 30 32 42 44 54 56 84 86	50463819630
SPT(16)	921769557074012861	0 2 42 48 90 128 146 152 216 222 240 278 320 326 366 368	838114269324
SPT(16)	921769563777366547	0 22 64 112 180 196 216 220 246 250 270 286 354 402 444 466	844817623010
SPT(16)	921769596444225541	0 42 46 60 132 138 168 178 210 220 250 256 328 342 346 388	877484482004
STPT(10)	921769816619686127	0 2 30 32 60 62 90 92 120 122	1097659942590