Prime p₀= 399494291176554401 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 28 2 76 2 28 2 10 2 (?)
a_n: 0 2 18 20 48 50 126 128 156 158 168 170
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, 16 28 76 28 10

SPT(14)	399494130114741023	0 8 68 96 98 110 194 300 384 396 398 426 486 494	-161061813378
TPT(12)	399494141111077697	0 2 12 14 24 26 60 62 102 104 150 152	-150065476704
SPT(14)	399494187830893703	0 14 20 36 48 56 108 116 168 176 188 204 210 224	-103345660698
SPT(14)	399494200486163317	0 22 36 82 90 112 150 166 204 226 234 280 294 316	-90690391084
SPT(14)	399494264544922879	0 10 30 40 48 70 72 118 120 142 150 160 180 190	-26631631522
SPT(14)	399494275999762511	0 78 80 86 122 126 128 150 152 156 192 198 200 278	-15176791890
SPT(14)	399494309716019029	0 10 18 94 124 130 142 150 162 168 198 274 282 292	18539464628
TPT(12)	399494314523646227	0 2 12 14 30 32 54 56 210 212 240 242	23347091826
SPT(14)	399494331887768329	0 60 70 90 102 130 150 172 192 220 232 252 262 322	40711213928
SPT(14)	399494352294381341	0 6 18 26 48 60 72 86 98 110 132 140 152 158	61117826940
SPT(14)	399494352477536189	0 14 42 48 54 90 108 224 242 278 284 290 318 332	61300981788