Prime p₀= 2949004563335933957 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 4 2 82 2 274 2 70 2 40 2 (?)
a_n: 0 2 24 26 30 32 114 116 390 392 462 464 504 506
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: 506
Found by: [SG-FC] hl
db: batch=82, k=14, 22 4 82 274 70 40

SPT(16)	2949002351161236031	0 12 18 30 72 112 132 142 156 166 186 226 268 280 286 298	-2212174697926
SPT(16)	2949002840498388127	0 24 46 102 114 174 180 216 220 256 262 322 334 390 412 436	-1722837545830
STPT(10)	2949002933086064597	0 2 12 14 42 44 72 74 84 86	-1630249869360
SPT(16)	2949002989749607837	0 12 34 40 54 96 142 244 252 354 400 442 456 462 484 496	-1573586326120
SPT(16)	2949003113883263321	0 2 48 98 140 212 230 240 290 300 318 390 432 482 528 530	-1449452670636
SPT(16)	2949004065568792657	0 30 66 70 114 154 166 184 192 210 222 262 306 310 346 376	-497767141300
TPT(14)	2949004756309637957	0 2 72 74 120 122 192 194 204 206 240 242 252 254	192973704000
SPT(16)	2949004803443023783	0 76 148 196 210 234 258 300 304 346 370 394 408 456 528 604	240107089826
SPT(16)	2949004805883825847	0 16 42 72 96 100 126 156 166 196 222 226 250 280 306 322	242547891890
TPT(14)	2949005113806027707	0 2 12 14 54 56 60 62 294 296 342 344 354 356	550470093750
STPT(10)	2949005220570915029	0 2 18 20 30 32 42 44 60 62	657234981072