Prime p₀= 86129420678087909 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 76 2 10 2 58 2 40 2 64 2 (?)
a_n: 0 2 78 80 90 92 150 152 192 194 258 260
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: 260
Found by: Paul
db: batch=67, k=12, 76 10 58 40 64

SPT(14)	86129333704602563	0 6 30 36 48 60 78 96 114 126 138 144 168 174	-86973485346
SPT(14)	86129371185122101	0 58 72 88 100 118 130 228 240 258 270 286 300 358	-49492965808
SPT(14)	86129398236176671	0 36 52 60 70 88 106 132 150 168 178 186 202 238	-22441911238
SPT(14)	86129408357501381	0 20 26 32 42 48 60 98 110 116 126 132 138 158	-12320586528
SPT(16)	86129409654344291	0 8 32 60 72 92 98 110 120 132 138 158 170 198 222 230	-11023743618
SPT(14)	86129413569056147	0 20 26 42 54 92 110 156 174 212 224 240 246 266	-7109031762
TPT(12)	86129421162832637	0 2 42 44 72 74 120 122 144 146 174 176	484744728
SPT(14)	86129433479028239	0 32 44 48 102 192 200 222 230 320 374 378 390 422	12800940330
SPT(14)	86129439923712191	0 26 32 42 90 102 108 140 146 158 206 216 222 248	19245624282
SPT(14)	86129442964184371	0 6 42 66 72 76 96 136 156 160 166 190 226 232	22286096462
SPT(14)	86129464812837659	0 42 48 50 90 98 108 122 132 140 180 182 188 230	44134749750