Prime p₀= 12444049932618221 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 4 2 28 2 58 2 40 2 (?)
a_n: 0 2 30 32 36 38 66 68 126 128 168 170
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: crashtech
db: batch=62, k=12, 28 4 28 58 40

TPT(12)	12444019932065387	0 2 12 14 30 32 72 74 120 122 162 164	-30000552834
SPT(14)	12444030519457673	0 6 38 110 126 134 140 174 180 188 204 276 308 314	-19413160548
SPT(20)	12444030951323113	0 16 36 48 58 64 70 90 114 148 156 190 214 234 240 246 256 268 288 304	-18981295108
SPT(14)	12444032781723871	0 30 58 72 118 126 130 138 142 150 196 210 238 268	-17150894350
SPT(14)	12444041307450419	0 2 8 14 50 60 120 122 182 192 228 234 240 242	-8625167802
SPT(14)	12444048078095597	0 56 62 90 96 144 150 176 182 230 236 264 270 326	-1854522624
SPT(14)	12444050399571149	0 2 14 42 72 78 104 108 134 140 170 198 210 212	466952928
SPT(14)	12444052249369529	0 38 54 62 92 120 224 228 332 360 390 398 414 452	2316751308
SPT(14)	12444058158956507	0 24 32 54 80 110 114 140 144 174 200 222 230 254	8226338286
SPT(14)	12444060736894621	0 30 52 72 90 132 150 160 178 220 238 258 280 310	10804276400
TPT(12)	12444110153054687	0 2 30 32 72 74 90 92 132 134 174 176	60220436466