Prime p₀= 1117632785901201527 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 34 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 60 62 72 74 84 86
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: 86
Found by: crashtech
db: batch=76, k=12, 2 10 2 10 2 34

SPT(16)	1117632158760508267	0 6 16 22 84 114 154 172 174 192 232 262 324 330 340 346	-627140693260
STPT(10)	1117632275409134039	0 2 42 44 60 62 78 80 120 122	-510492067488
SPT(16)	1117632276307073557	0 16 34 66 94 130 144 184 186 226 240 276 304 336 354 370	-509594127970
SPT(16)	1117632436510180183	0 6 10 48 84 94 106 108 136 138 150 160 196 234 238 244	-349391021344
STPT(12)	1117632586426426949	0 2 72 74 102 104 138 140 168 170 240 242	-199474774578
TPT(14)	1117632785901201509	0 2 18 20 30 32 42 44 78 80 90 92 102 104	-18
SPT(16)	1117633021810135123	0 28 40 46 54 60 66 88 96 118 124 130 138 144 156 184	235908933596
SPT(16)	1117633122392806127	0 6 20 54 92 132 140 150 206 216 224 264 302 336 350 356	336491604600
SPT(16)	1117633538460541463	0 6 18 20 50 98 128 140 174 186 216 264 294 296 308 314	752559339936
STPT(10)	1117633690541956499	0 2 18 20 30 32 42 44 60 62	904640754972
SPT(16)	1117634004076575697	0 12 40 54 70 112 126 132 154 160 174 216 232 246 274 286	1218175374170