Prime p₀= 2726443498105540307 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 52 2 28 2 4 2 28 2 52 2 (?)
a_n: 0 2 54 56 84 86 90 92 120 122 174 176
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 176
Found by: Cruncher Pete
db: batch=82, k=12, 2 52 2 28 2 4

SPT(16)	2726441478048339313	0 30 40 54 100 126 174 196 204 226 274 300 346 360 370 400	-2020057200994
TPT(14)	2726441750192843861	0 2 36 38 66 68 90 92 126 128 138 140 330 332	-1747912696446
STPT(10)	2726442285834466889	0 2 18 20 30 32 42 44 60 62	-1212271073418
STPT(10)	2726442522235994447	0 2 30 32 72 74 114 116 144 146	-975869545860
STPT(10)	2726443227695451611	0 2 6 8 48 50 90 92 96 98	-270410088696
SPT(16)	2726443321627199159	0 44 68 84 90 122 170 174 188 192 240 272 278 294 318 362	-176478341148
STPT(10)	2726443559532607307	0 2 30 32 42 44 54 56 84 86	61427067000
SPT(16)	2726444993494671353	0 6 20 24 38 56 98 108 146 156 198 216 230 234 248 254	1495389131046
SPT(16)	2726445043048469023	0 4 24 54 78 124 144 178 240 274 294 340 364 394 414 418	1544942928716
STPT(10)	2726445421081884989	0 2 48 50 90 92 132 134 180 182	1922976344682
SPT(16)	2726445461444054557	0 4 30 34 60 76 100 216 250 366 390 406 432 436 462 466	1963338514250