Prime p₀= 1497338776799954729 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 16 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 60 62 90 92 102 104
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: 104
Found by: Spectrum
db: batch=78, k=12, 2 10 2 28 2 16

SPT(16)	1497337027977497867	0 20 56 62 86 96 102 116 180 194 200 210 234 240 276 296	-1748822456862
STPT(10)	1497337401293522417	0 2 30 32 72 74 114 116 144 146	-1375506432312
SPT(16)	1497337449042776711	0 30 60 96 122 126 128 152 186 210 212 216 242 278 308 338	-1327757178018
STPT(10)	1497337708985738297	0 2 30 32 42 44 54 56 84 86	-1067814216432
SPT(16)	1497337982860033109	0 24 48 60 102 132 152 158 174 180 200 230 272 284 308 332	-793939921620
SPT(16)	1497338698080965083	0 4 40 70 136 168 186 270 304 388 406 438 504 534 570 574	-78718989646
STPT(10)	1497339091102805771	0 2 6 8 18 20 30 32 36 38	314302851042
TPT(14)	1497339549965272367	0 2 12 14 54 56 144 146 180 182 210 212 222 224	773165317638
STPT(10)	1497339607616341439	0 2 18 20 30 32 42 44 60 62	830816386710
SPT(16)	1497339623683990649	0 2 12 38 44 80 104 114 188 198 222 258 264 290 300 302	846884035920
SPT(16)	1497340333670028611	0 32 78 98 102 126 168 176 312 320 362 386 390 410 456 488	1556870073882