Prime p₀= 2276096297992984109 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 58 2 4 2 58 2 40 2 (?)
a_n: 0 2 42 44 102 104 108 110 168 170 210 212
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: 212
Found by: Landjunge
db: batch=81, k=12, 2 40 2 58 2 4

SPT(16)	2276095936083035191	0 48 60 72 88 138 180 208 270 298 340 390 406 418 430 478	-361909948918
STPT(10)	2276095976543331359	0 2 18 20 30 32 42 44 60 62	-321449652750
SPT(18)	2276096122535438807	0 14 24 60 84 90 120 146 164 186 204 230 260 266 290 326 336 350	-175457545302
SPT(16)	2276096166180074593	0 4 6 24 46 66 70 106 108 144 148 168 190 208 210 214	-131812909516
SPT(16)	2276096216686146493	0 16 66 78 84 100 108 114 190 196 204 220 226 238 288 304	-81306837616
SPT(16)	2276096266897763161	0 36 42 48 66 70 76 148 150 222 228 232 250 256 262 298	-31095220948
STPT(10)	2276096324862441797	0 2 42 44 72 74 102 104 144 146	26869457688
STPT(10)	2276096660417964677	0 2 42 44 72 74 102 104 144 146	362424980568
STPT(10)	2276096748936407597	0 2 30 32 72 74 114 116 144 146	450943423488
TPT(14)	2276096866410300119	0 2 18 20 180 182 312 314 348 350 378 380 390 392	568417316010
SPT(16)	2276096868769106039	0 38 42 48 68 132 140 180 182 222 230 294 314 320 324 362	570776121930