Prime p₀= 338322380224799669 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 52 2 136 2 58 2 46 2 (?)
a_n: 0 2 18 20 72 74 210 212 270 272 318 320
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: 320
Found by: Cruncher Pete
db: batch=70, k=12, 16 52 136 58 46

SPT(14)	338322280214890087	0 12 46 72 84 96 102 154 160 172 184 210 244 256	-100009909582
SPT(14)	338322296343046837	0 40 84 90 120 150 154 216 220 250 280 286 330 370	-83881752832
SPT(14)	338322302433357013	0 4 46 76 94 118 126 178 186 210 228 258 300 304	-77791442656
SPT(14)	338322305539253227	0 10 30 70 90 132 136 216 220 262 282 322 342 352	-74685546442
SPT(14)	338322316113683219	0 24 50 90 92 110 120 152 162 180 182 222 248 272	-64111116450
SPT(14)	338322360799612831	0 6 12 46 78 96 118 180 202 220 252 286 292 298	-19425186838
SPT(16)	338322384653380123	0 24 58 64 76 78 100 126 148 174 196 198 210 216 250 274	4428580454
SPT(14)	338322395975555951	0 12 38 66 86 116 152 156 192 222 242 270 296 308	15750756282
SPT(14)	338322401857041871	0 16 42 52 66 70 96 136 162 166 180 190 216 232	21632242202
SPT(14)	338322422438659861	0 12 46 72 90 102 132 166 196 208 226 252 286 298	42213860192
SPT(14)	338322424399140143	0 44 56 68 98 138 140 144 146 186 216 228 240 284	44174340474