Prime p₀= 2999084709303919667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 250 2 70 2 136 2 10 2 34 2 40 2 (?)
a_n: 0 2 252 254 324 326 462 464 474 476 510 512 552 554
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: 554
Found by: fake
db: batch=82, k=14, 250 70 136 10 34 40

SPT(16)	2999082818287496921	0 2 32 38 66 78 120 168 200 248 290 302 330 336 366 368	-1891016422746
SPT(16)	2999083007690719891	0 12 28 78 90 118 142 156 172 186 210 238 250 300 316 328	-1701613199776
SPT(16)	2999083442901559213	0 48 88 90 186 208 228 246 418 436 456 478 574 576 616 664	-1266402360454
STPT(10)	2999083697330410169	0 2 18 20 30 32 42 44 60 62	-1011973509498
SPT(16)	2999084076909360001	0 16 52 66 70 100 102 156 172 226 228 258 262 276 312 328	-632394559666
SPT(16)	2999084627502865883	0 18 56 80 98 104 128 144 170 186 210 216 234 258 296 314	-81801053784
SPT(16)	2999085517992822649	0 72 160 174 210 244 264 282 310 328 348 382 418 432 520 592	808688902982
STPT(10)	2999085734839126481	0 2 6 8 48 50 90 92 96 98	1025535206814
STPT(10)	2999086453676989799	0 2 12 14 30 32 48 50 60 62	1744373070132
STPT(10)	2999087040970800851	0 2 36 38 78 80 120 122 156 158	2331666881184
SPT(16)	2999087066889928387	0 24 36 60 106 112 150 156 190 196 234 240 286 310 322 346	2357586008720