Prime p₀= 3000113671233289727 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 40 2 88 2 4 2 28 2 (?)
a_n: 0 2 30 32 42 44 84 86 174 176 180 182 210 212
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: 212
Found by: Coleslaw
db: batch=82, k=14, 28 10 40 88 4 28

SPT(16)	3000113045432451463	0 54 58 60 78 114 184 190 204 210 280 316 334 336 340 394	-625800838264
STPT(10)	3000113088842571587	0 2 30 32 72 74 114 116 144 146	-582390718140
SPT(16)	3000113235706041991	0 48 60 82 130 138 160 180 238 258 280 288 336 358 370 418	-435527247736
SPT(16)	3000113374293914899	0 34 60 82 114 118 130 132 250 252 264 268 300 322 348 382	-296939374828
TPT(14)	3000113382706196147	0 2 24 26 54 56 72 74 84 86 144 146 180 182	-288527093580
SPT(16)	3000113552765604211	0 16 126 132 198 210 222 258 370 406 418 430 496 502 612 628	-118467685516
STPT(10)	3000113895054851147	0 2 24 26 42 44 60 62 84 86	223821561420
STPT(10)	3000113945046180617	0 2 12 14 72 74 132 134 144 146	273812890890
STPT(10)	3000114213017518691	0 2 6 8 48 50 90 92 96 98	541784228964
TPT(14)	3000114280319698427	0 2 12 14 42 44 54 56 174 176 240 242 462 464	609086408700
SPT(16)	3000114447671558467	0 6 22 52 70 82 90 216 250 376 384 396 414 444 460 466	776438268740