Prime p₀= 2048975407484003267 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 58 2 64 2 22 2 46 2 28 2 (?)
a_n: 0 2 24 26 84 86 150 152 174 176 222 224 252 254
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: 254
Found by: Coleslaw
db: batch=80, k=14, 22 58 64 22 46 28

SPT(16)	2048974444165277711	0 12 18 36 42 108 146 176 192 222 260 326 332 350 356 368	-963318725556
STPT(10)	2048974848800009927	0 2 24 26 42 44 60 62 84 86	-558683993340
SPT(16)	2048974998889243673	0 6 26 36 48 80 134 138 176 180 234 266 278 288 308 314	-408594759594
SPT(16)	2048975293200300433	0 64 70 90 94 124 138 150 178 190 204 234 238 258 264 328	-114283702834
SPT(16)	2048975298646275719	0 14 42 44 128 140 168 194 258 284 312 324 408 410 438 452	-108837727548
SPT(16)	2048975328786001579	0 52 90 108 112 120 172 174 208 210 262 270 274 292 330 382	-78698001688
SPT(16)	2048975628800272979	0 14 24 32 48 132 140 162 170 192 200 284 300 308 318 332	221316269712
SPT(16)	2048975699026704641	0 26 62 68 90 98 128 186 212 270 300 308 330 336 372 398	291542701374
SPT(16)	2048975975016521227	0 22 42 54 70 112 132 136 150 154 174 216 232 244 264 286	567532517960
SPT(16)	2048976460715500669	0 40 168 184 190 238 294 300 358 364 420 468 474 490 618 658	1053231497402
SPT(16)	2048976939139601059	0 4 10 18 28 42 52 84 88 120 130 144 154 162 168 172	1531655597792