Prime p₀= 1013235638725790021 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 34 2 10 2 28 2 10 2 34 2 (?)
a_n: 0 2 36 38 48 50 78 80 90 92 126 128
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: 128
Found by: HenkM
db: batch=76, k=12, 2 34 2 10 2 28

SPT(16)	1013233856120838031	0 10 12 102 148 172 180 198 220 238 246 270 316 406 408 418	-1782604951990
SPT(16)	1013234188335491443	0 10 16 24 66 76 100 154 180 234 258 268 310 318 324 334	-1450390298578
STPT(10)	1013234228991134609	0 2 18 20 30 32 42 44 60 62	-1409734655412
SPT(16)	1013234452317652771	0 40 72 90 118 142 162 192 208 238 258 282 310 328 360 400	-1186408137250
STPT(10)	1013235366610959431	0 2 30 32 60 62 90 92 120 122	-272114830590
SPT(16)	1013235385951206589	0 12 54 72 78 100 112 124 138 150 162 184 190 208 250 262	-252774583432
SPT(16)	1013236724893490051	0 26 42 50 56 78 146 152 276 282 350 372 378 386 402 428	1086167700030
SPT(16)	1013236814034238601	0 8 42 48 108 126 140 150 188 198 212 230 290 296 330 338	1175308448580
SPT(16)	1013237291508215479	0 40 54 70 144 184 210 228 304 322 348 388 462 478 492 532	1652782425458
STPT(10)	1013237321245305599	0 2 42 44 60 62 78 80 120 122	1682519515578
STPT(12)	1013237793236030561	0 2 6 8 78 80 138 140 210 212 216 218	2154510240540