Prime p₀= 2799125446890679799 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 52 2 34 2 88 2 28 2 10 2 (?)
a_n: 0 2 48 50 102 104 138 140 228 230 258 260 270 272
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: 272
Found by: JayPi
db: batch=82, k=14, 46 52 34 88 28 10

SPT(16)	2799123403160229799	0 10 24 54 154 162 198 208 264 274 310 318 418 448 462 472	-2043730450000
STPT(10)	2799123568488732311	0 2 30 32 78 80 126 128 156 158	-1878401947488
STPT(10)	2799124020240645947	0 2 54 56 132 134 210 212 264 266	-1426650033852
STPT(10)	2799124457639419937	0 2 24 26 42 44 60 62 84 86	-989251259862
SPT(16)	2799124735201147097	0 6 26 42 50 84 90 110 156 176 182 216 224 240 260 266	-711689532702
SPT(16)	2799124758147408391	0 10 30 70 106 126 136 142 156 162 172 192 228 268 288 298	-688743271408
TPT(14)	2799125918648968121	0 2 36 38 48 50 276 278 288 290 300 302 336 338	471758288322
SPT(16)	2799126788680319087	0 50 74 90 92 104 126 210 236 320 342 354 356 372 396 446	1341789639288
STPT(10)	2799126892562481449	0 2 12 14 90 92 168 170 180 182	1445671801650
STPT(10)	2799126959218192781	0 2 6 8 48 50 90 92 96 98	1512327512982
SPT(16)	2799127228088869939	0 10 22 24 52 60 88 118 144 174 202 210 238 240 252 262	1781198190140