Prime p₀= 2736043093270391039 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 58 2 22 2 28 2 34 2 40 2 (?)
a_n: 0 2 18 20 78 80 102 104 132 134 168 170 210 212
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: [SG-2W]Kurzer
db: batch=82, k=14, 16 58 22 28 34 40

SPT(16)	2736041793592313797	0 6 12 40 52 90 162 220 276 334 406 444 456 484 490 496	-1299678077242
STPT(10)	2736041911832629187	0 2 60 62 72 74 84 86 144 146	-1181437761852
TPT(14)	2736042360296679491	0 2 30 32 336 338 360 362 366 368 378 380 408 410	-732973711548
SPT(16)	2736042502242846169	0 24 64 72 90 154 168 174 178 184 198 262 280 288 328 352	-591027544870
SPT(16)	2736042579140045159	0 32 54 140 144 180 218 222 230 234 272 308 312 398 420 452	-514130345880
SPT(16)	2736042845866586687	0 62 74 90 92 96 144 146 210 212 260 264 266 282 294 356	-247403804352
STPT(10)	2736043364756246747	0 2 42 44 72 74 102 104 144 146	271485855708
STPT(10)	2736043414891514081	0 2 6 8 48 50 90 92 96 98	321621123042
STPT(10)	2736043568850082607	0 2 54 56 132 134 210 212 264 266	475579691568
SPT(16)	2736043638446738339	0 20 62 102 110 152 170 200 252 282 300 342 350 390 432 452	545176347300
SPT(16)	2736044343666789481	0 40 46 58 102 106 112 162 166 216 222 226 270 282 288 328	1250396398442