Prime p₀= 346418232674399621 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 34 2 70 2 28 2 16 2 10 2 (?)
a_n: 0 2 36 38 108 110 138 140 156 158 168 170
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: 170
Found by: Cruncher Pete
db: batch=70, k=12, 34 70 28 16 10

SPT(14)	346418179975835767	0 16 64 90 100 112 174 262 324 336 346 372 420 436	-52698563854
SPT(14)	346418189810445149	0 24 50 62 74 80 92 192 204 210 222 234 260 284	-42863954472
SPT(14)	346418192482727557	0 12 22 40 64 82 96 100 114 132 156 174 184 196	-40191672064
SPT(14)	346418195503570759	0 10 22 34 70 108 148 204 244 282 318 330 342 352	-37170828862
TPT(12)	346418206283851577	0 2 72 74 150 152 192 194 204 206 210 212	-26390548044
SPT(14)	346418231343564253	0 4 16 40 48 54 60 124 130 136 144 168 180 184	-1330835368
SPT(14)	346418234301124877	0 14 20 30 42 72 86 90 104 134 146 156 162 176	1626725256
TPT(12)	346418237604009917	0 2 12 14 54 56 132 134 150 152 162 164	4929610296
SPT(14)	346418243322301567	0 30 82 84 96 102 126 130 154 160 172 174 226 256	10647901946
SPT(16)	346418259111611591	0 6 20 36 90 116 120 150 266 296 300 326 380 396 410 416	26437211970
SPT(14)	346418260745611253	0 14 38 50 80 108 140 174 206 234 264 276 300 314	28071211632