Prime p₀= 186576672112416167 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 58 2 76 2 28 2 40 2 (?)
a_n: 0 2 24 26 84 86 162 164 192 194 234 236
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: 236
Found by: desktop64
db: batch=69, k=12, 22 58 76 28 40

SPT(14)	186576588438777833	0 36 38 114 116 126 128 156 158 168 170 246 248 284	-83673638334
STPT(12)	186576588438777869	0 2 78 80 90 92 120 122 132 134 210 212	-83673638298
TPT(12)	186576588438777869	0 2 78 80 90 92 120 122 132 134 210 212	-83673638298
TPT(12)	186576589068190829	0 2 72 74 132 134 222 224 228 230 258 260	-83044225338
STPT(10)	186576591944954051	0 2 36 38 78 80 120 122 156 158	-80167462116
SPT(16)	186576646545493297	0 10 42 120 156 172 186 190 282 286 300 316 352 430 462 472	-25566922870
SPT(14)	186576690399096367	0 10 12 96 132 142 156 196 210 220 256 340 342 352	18286680200
SPT(14)	186576696002330831	0 26 32 66 108 120 138 140 158 170 212 246 252 278	23889914664
SPT(14)	186576709194149383	0 30 36 54 84 126 130 180 184 226 256 274 280 310	37081733216
SPT(14)	186576714303553571	0 32 72 78 128 138 162 176 200 210 260 266 306 338	42191137404
SPT(14)	186576716638560307	0 22 30 42 54 72 82 114 124 142 154 166 174 196	44526144140