Prime p₀= 432728849852156309 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 100 2 64 2 100 2 10 2 124 2 (?)
a_n: 0 2 102 104 168 170 270 272 282 284 408 410
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: 410
Found by: Cruncher Pete
db: batch=70, k=12, 100 64 100 10 124

SPT(14)	432728726801353373	0 6 14 20 24 26 56 108 138 140 144 150 158 164	-123050802936
SPT(14)	432728726811777257	0 42 50 56 72 96 110 186 200 224 240 246 254 296	-123040379052
SPT(16)	432728744413191209	0 68 90 92 104 198 222 230 252 260 284 378 390 392 414 482	-105438965100
SPT(14)	432728768526034483	0 40 48 114 136 154 156 178 180 198 220 286 294 334	-81326121826
TPT(12)	432728782686310499	0 2 30 32 48 50 72 74 102 104 180 182	-67165845810
SPT(14)	432728810558094689	0 30 60 90 122 140 162 170 192 210 242 272 302 332	-39294061620
STPT(10)	432728864576585849	0 2 18 20 30 32 42 44 60 62	14724429540
SPT(14)	432728883550682737	0 6 12 16 72 90 100 156 166 184 240 244 250 256	33698526428
TPT(12)	432728905673837387	0 2 30 32 42 44 60 62 240 242 270 272	55821681078
SPT(14)	432728915468618149	0 40 58 78 82 90 108 124 142 150 154 174 192 232	65616461840
TPT(12)	432728925267689381	0 2 6 8 36 38 48 50 60 62 168 170	75415533072