Prime p₀= 1304811964602354119 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 16 2 10 2 16 2 40 2 (?)
a_n: 0 2 42 44 60 62 72 74 90 92 132 134
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: 134
Found by: [SG-2W]Kurzer
db: batch=77, k=12, 2 40 2 16 2 10

STPT(10)	1304811049169280941	0 2 36 38 78 80 120 122 156 158	-915433073178
STPT(10)	1304811491226383207	0 2 12 14 72 74 132 134 144 146	-473375970912
TPT(14)	1304811571466872289	0 2 18 20 120 122 132 134 210 212 252 254 270 272	-393135481830
SPT(16)	1304811612636849677	0 20 50 84 104 132 162 204 260 302 332 360 380 414 444 464	-351965504442
TPT(14)	1304811765843847379	0 2 18 20 42 44 108 110 360 362 462 464 570 572	-198758506740
SPT(16)	1304811935241119339	0 12 20 72 108 152 158 188 192 222 228 272 308 360 368 380	-29361234780
STPT(14)	1304811990580936037	0 2 30 32 54 56 72 74 90 92 114 116 144 146	25978581918
TPT(14)	1304811990580936037	0 2 30 32 54 56 72 74 90 92 114 116 144 146	25978581918
SPT(16)	1304812733321527069	0 12 34 48 52 54 72 84 148 160 178 180 184 198 220 232	768719172950
SPT(16)	1304813081848198231	0 28 36 112 130 138 166 178 180 192 220 228 246 322 330 358	1117245844112
STPT(10)	1304813140555694051	0 2 78 80 168 170 258 260 336 338	1175953339932