Prime p₀= 1268810796161597231 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 4 2 40 2 88 2 40 2 4 2 (?)
a_n: 0 2 6 8 48 50 138 140 180 182 186 188
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: 188
Found by: Megacruncher
db: batch=77, k=12, 2 4 2 40 2 88

SPT(16)	1268809575246985769	0 30 54 60 128 140 194 200 222 228 282 294 362 368 392 422	-1220914611462
SPT(16)	1268809621754708513	0 8 50 68 120 140 194 198 236 240 294 314 366 384 426 434	-1174406888718
SPT(16)	1268810142051884143	0 24 64 66 76 78 84 136 288 340 346 348 358 360 400 424	-654109713088
SPT(16)	1268810467337962531	0 16 22 58 78 82 112 138 220 246 276 280 300 336 342 358	-328823634700
STPT(10)	1268810608779163361	0 2 6 8 18 20 30 32 36 38	-187382433870
SPT(18)	1268810664193391329	0 142 148 162 168 174 190 204 220 222 238 252 268 274 280 294 300 442	-131968205902
TPT(14)	1268810840309167709	0 2 72 74 180 182 240 242 288 290 378 380 402 404	44147570478
SPT(20)	1268810872306770797	0 2 6 20 56 92 102 134 156 170 186 200 222 254 264 300 336 350 354 356	76145173566
SPT(16)	1268810968191034357	0 6 22 36 52 70 84 94 102 112 126 144 160 174 190 196	172029437126
STPT(10)	1268811410744561657	0 2 30 32 42 44 54 56 84 86	614582964426
SPT(16)	1268811696866993011	0 12 28 40 66 106 160 250 258 348 402 442 468 480 496 508	900705395780