Prime p₀= 1097085004753746581 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 16 2 40 2 4 2 40 2 16 2 (?)
a_n: 0 2 18 20 60 62 66 68 108 110 126 128
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: [SG-2W]Kurzer
db: batch=76, k=12, 2 16 2 40 2 4

SPT(16)	1097083728919940917	0 12 30 36 96 106 112 114 232 234 240 250 310 316 334 346	-1275833805664
TPT(14)	1097084092445267609	0 2 12 14 42 44 102 104 180 182 270 272 282 284	-912308478972
SPT(16)	1097084205800800643	0 20 30 66 74 86 114 156 308 350 378 390 398 434 444 464	-798952945938
STPT(10)	1097084482245517691	0 2 30 32 78 80 126 128 156 158	-522508228890
TPT(14)	1097084823711362987	0 2 42 44 72 74 114 116 222 224 270 272 282 284	-181042383594
SPT(16)	1097084978370024521	0 12 36 50 56 78 96 98 150 152 170 192 198 212 236 248	-26383722060
SPT(16)	1097085238021586861	0 6 20 26 78 98 110 152 246 288 300 320 372 378 392 398	233267840280
SPT(16)	1097085329832997369	0 18 112 132 138 142 184 190 222 228 270 274 280 300 394 412	325079250788
STPT(10)	1097085393033896657	0 2 30 32 42 44 54 56 84 86	388280150076
TPT(14)	1097085404090502677	0 2 30 32 42 44 102 104 132 134 144 146 222 224	399336756096
STPT(10)	1097085525889486751	0 2 36 38 78 80 120 122 156 158	521135740170