Prime p₀= 10577892025407557 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 40 2 34 2 22 2 16 2 (?)
a_n: 0 2 12 14 54 56 90 92 114 116 132 134
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: 134
Found by: crashtech
db: batch=62, k=12, 10 40 34 22 16

SPT(14)	10577855723536979	0 8 14 44 54 78 138 170 230 254 264 294 300 308	-36301870578
SPT(14)	10577860168590901	0 58 70 106 112 120 142 186 208 216 222 258 270 328	-31856816656
SPT(16)	10577861594698549	0 12 22 42 82 84 88 138 154 204 208 210 250 270 280 292	-30430709008
SPT(14)	10577863530036059	0 8 14 20 38 80 104 138 162 204 222 228 234 242	-28495371498
SPT(14)	10577879266729009	0 42 58 78 112 114 160 162 208 210 244 264 280 322	-12758678548
TPT(12)	10577880820107437	0 2 12 14 72 74 114 116 174 176 180 182	-11205300120
TPT(12)	10577892543071729	0 2 12 14 72 74 108 110 150 152 168 170	517664172
SPT(14)	10577893475952421	0 10 22 40 42 82 138 190 246 286 288 306 318 328	1450544864
TPT(14)	10577911955974499	0 2 12 14 42 44 48 50 108 110 120 122 132 134	19930566942
SPT(14)	10577923170543017	0 14 24 44 50 66 80 90 104 120 126 146 156 170	31145135460
SPT(14)	10577929466119507	0 6 10 34 72 90 114 172 196 214 252 276 280 286	37440711950