Prime p₀= 1117632586426426949 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 70 2 28 2 34 2 28 2 70 2 (?)
a_n: 0 2 72 74 102 104 138 140 168 170 240 242
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: 242
Found by: crashtech
db: batch=76, k=12, 2 70 2 28 2 34

SPT(16)	1117631910132478703	0 8 36 84 86 140 158 216 308 366 384 438 440 488 516 524	-676293948246
TPT(14)	1117631960160992249	0 2 30 32 42 44 78 80 150 152 162 164 198 200	-626265434700
SPT(16)	1117632158760508267	0 6 16 22 84 114 154 172 174 192 232 262 324 330 340 346	-427665918682
STPT(10)	1117632275409134039	0 2 42 44 60 62 78 80 120 122	-311017292910
SPT(16)	1117632276307073557	0 16 34 66 94 130 144 184 186 226 240 276 304 336 354 370	-310119353392
SPT(16)	1117632436510180183	0 6 10 48 84 94 106 108 136 138 150 160 196 234 238 244	-149916246766
TPT(14)	1117632785901201509	0 2 18 20 30 32 42 44 78 80 90 92 102 104	199474774560
STPT(12)	1117632785901201527	0 2 12 14 24 26 60 62 72 74 84 86	199474774578
SPT(16)	1117633021810135123	0 28 40 46 54 60 66 88 96 118 124 130 138 144 156 184	435383708174
SPT(16)	1117633122392806127	0 6 20 54 92 132 140 150 206 216 224 264 302 336 350 356	535966379178
SPT(16)	1117633538460541463	0 6 18 20 50 98 128 140 174 186 216 264 294 296 308 314	952034114514