Prime p₀= 86129421162832637 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 28 2 46 2 22 2 28 2 (?)
a_n: 0 2 42 44 72 74 120 122 144 146 174 176
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: 176
Found by: Paul
db: batch=67, k=12, 40 28 46 22 28

SPT(14)	86129371185122101	0 58 72 88 100 118 130 228 240 258 270 286 300 358	-49977710536
SPT(14)	86129398236176671	0 36 52 60 70 88 106 132 150 168 178 186 202 238	-22926655966
SPT(14)	86129408357501381	0 20 26 32 42 48 60 98 110 116 126 132 138 158	-12805331256
SPT(16)	86129409654344291	0 8 32 60 72 92 98 110 120 132 138 158 170 198 222 230	-11508488346
SPT(14)	86129413569056147	0 20 26 42 54 92 110 156 174 212 224 240 246 266	-7593776490
TPT(12)	86129420678087909	0 2 78 80 90 92 150 152 192 194 258 260	-484744728
SPT(14)	86129433479028239	0 32 44 48 102 192 200 222 230 320 374 378 390 422	12316195602
SPT(14)	86129439923712191	0 26 32 42 90 102 108 140 146 158 206 216 222 248	18760879554
SPT(14)	86129442964184371	0 6 42 66 72 76 96 136 156 160 166 190 226 232	21801351734
SPT(14)	86129464812837659	0 42 48 50 90 98 108 122 132 140 180 182 188 230	43650005022
SPT(14)	86129471248467419	0 2 62 68 80 108 132 170 194 222 234 240 300 302	50085634782