Prime p₀= 4365136052108060039 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 40 2 34 2 40 2 28 2 (?)
a_n: 0 2 30 32 72 74 108 110 150 152 180 182
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: 182
Found by: Autofuzzy
db: batch=85, k=12, 2 28 2 40 2 34

SPT(16)	4365135306852297739	0 24 28 58 72 84 132 142 150 160 208 220 234 264 268 292	-745255762300
SPT(16)	4365135352716484981	0 10 60 120 162 186 220 270 298 348 382 406 448 508 558 568	-699391575058
STPT(10)	4365135552513142499	0 2 78 80 120 122 162 164 240 242	-499594917540
SPT(16)	4365135608512412711	0 38 42 50 60 80 108 162 206 260 288 308 318 326 330 368	-443595647328
SPT(16)	4365135658770704569	0 22 58 70 78 90 100 148 174 222 232 244 252 264 300 322	-393337355470
SPT(16)	4365135906385822753	0 30 96 124 126 136 154 160 174 180 198 208 210 238 304 334	-145722237286
STPT(10)	4365136262371067789	0 2 12 14 90 92 168 170 180 182	210263007750
SPT(16)	4365136304636196637	0 60 70 100 126 132 160 172 174 186 214 220 246 276 286 346	252528136598
SPT(16)	4365136434615929279	0 20 42 48 62 72 164 192 230 258 350 360 374 380 402 422	382507869240
SPT(16)	4365136604167415771	0 32 90 92 132 156 158 182 246 270 272 296 336 338 396 428	552059355732
SPT(18)	4365136768706293631	0 32 42 56 90 98 102 120 146 162 188 206 210 218 252 266 276 308	716598233592