Prime p₀= 10577892543071729 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 58 2 34 2 40 2 16 2 (?)
a_n: 0 2 12 14 72 74 108 110 150 152 168 170
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, 10 58 34 40 16

SPT(14)	10577860168590901	0 58 70 106 112 120 142 186 208 216 222 258 270 328	-32374480828
SPT(16)	10577861594698549	0 12 22 42 82 84 88 138 154 204 208 210 250 270 280 292	-30948373180
SPT(14)	10577863530036059	0 8 14 20 38 80 104 138 162 204 222 228 234 242	-29013035670
SPT(14)	10577879266729009	0 42 58 78 112 114 160 162 208 210 244 264 280 322	-13276342720
TPT(12)	10577880820107437	0 2 12 14 72 74 114 116 174 176 180 182	-11722964292
TPT(12)	10577892025407557	0 2 12 14 54 56 90 92 114 116 132 134	-517664172
SPT(14)	10577893475952421	0 10 22 40 42 82 138 190 246 286 288 306 318 328	932880692
TPT(14)	10577911955974499	0 2 12 14 42 44 48 50 108 110 120 122 132 134	19412902770
SPT(14)	10577923170543017	0 14 24 44 50 66 80 90 104 120 126 146 156 170	30627471288
SPT(14)	10577929466119507	0 6 10 34 72 90 114 172 196 214 252 276 280 286	36923047778
SPT(14)	10577931619945471	0 48 60 70 78 88 108 130 150 160 168 178 190 238	39076873742