Prime p₀= 2726394103412570807 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 46 2 88 2 82 2 28 2 4 2 (?)
a_n: 0 2 12 14 60 62 150 152 234 236 264 266 270 272
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: Cruncher Pete
db: batch=82, k=14, 10 46 88 82 28 4

SPT(16)	2726392919474441741	0 18 30 72 200 212 216 222 326 332 336 348 476 518 530 548	-1183938129066
STPT(10)	2726393175460917887	0 2 12 14 42 44 72 74 84 86	-927951652920
TPT(14)	2726393249689482599	0 2 18 20 48 50 72 74 78 80 90 92 120 122	-853723088208
SPT(13)	2726393723327490157	0 12 42 54 90 120 132 144 174 210 222 252 264	-380085080650
STPT(10)	2726393870922445817	0 2 30 32 60 62 90 92 120 122	-232490124990
SPT(16)	2726393891365177001	0 2 26 62 96 122 168 180 308 320 366 392 426 462 486 488	-212047393806
STPT(10)	2726395016739086897	0 2 12 14 42 44 72 74 84 86	913326516090
SPT(16)	2726395227589550051	0 72 80 98 120 132 170 188 192 210 248 260 282 300 308 380	1124176979244
STPT(10)	2726395874828763131	0 2 36 38 78 80 120 122 156 158	1771416192324
STPT(10)	2726395975514941031	0 2 30 32 78 80 126 128 156 158	1872102370224
TPT(14)	2726396054165327051	0 2 30 32 96 98 156 158 258 260 366 368 396 398	1950752756244