Prime p₀= 432728925267689381 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 4 2 28 2 10 2 10 2 106 2 (?)
a_n: 0 2 6 8 36 38 48 50 60 62 168 170
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, 4 28 10 10 106

SPT(14)	432728810558094689	0 30 60 90 122 140 162 170 192 210 242 272 302 332	-114709594692
TPT(12)	432728849852156309	0 2 102 104 168 170 270 272 282 284 408 410	-75415533072
STPT(10)	432728864576585849	0 2 18 20 30 32 42 44 60 62	-60691103532
SPT(14)	432728883550682737	0 6 12 16 72 90 100 156 166 184 240 244 250 256	-41717006644
TPT(12)	432728905673837387	0 2 30 32 42 44 60 62 240 242 270 272	-19593851994
SPT(14)	432728915468618149	0 40 58 78 82 90 108 124 142 150 154 174 192 232	-9799071232
SPT(14)	432728940817574663	0 6 14 38 140 146 150 164 168 174 276 300 308 314	15549885282
SPT(14)	432729003432661843	0 40 78 108 120 130 138 178 186 196 208 238 276 316	78164972462
SPT(14)	432729003664629037	0 36 60 72 84 90 132 144 186 192 204 216 240 276	78396939656
SPT(14)	432729038830697351	0 2 26 78 80 92 96 182 186 198 200 252 276 278	113563007970
SPT(14)	432729046741788869	0 8 14 20 30 42 44 78 80 92 102 108 114 122	121474099488