Prime p₀= 112704883409503967 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 82 2 28 2 148 2 136 2 16 2 (?)
a_n: 0 2 84 86 114 116 264 266 402 404 420 422
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: 422
Found by: emoga
db: batch=67, k=12, 82 28 148 136 16

SPT(14)	112704785778160501	0 6 16 28 30 118 148 198 228 316 318 330 340 346	-97631343466
SPT(14)	112704802185944399	0 2 12 54 74 78 92 120 134 138 158 200 210 212	-81223559568
SPT(14)	112704806710087957	0 24 46 60 84 126 136 204 214 256 280 294 316 340	-76699416010
TPT(12)	112704840000197321	0 2 126 128 156 158 198 200 258 260 288 290	-43409306646
SPT(14)	112704843467534509	0 10 28 58 78 118 120 142 144 184 204 234 252 262	-39941969458
SPT(14)	112704880381965559	0 24 58 64 72 90 100 162 172 190 198 204 238 262	-3027538408
SPT(14)	112704884906502799	0 10 40 42 54 130 150 172 192 268 280 282 312 322	1496998832
SPT(14)	112704897149211527	0 42 80 102 132 150 156 266 272 290 320 342 380 422	13739707560
SPT(14)	112704902670791623	0 10 30 66 84 106 124 150 168 190 208 244 264 274	19261287656
SPT(14)	112704915136541639	0 14 38 42 62 92 104 108 120 150 170 174 198 212	31727037672
SPT(14)	112704935884650367	0 24 82 84 102 124 130 174 180 202 220 222 280 304	52475146400