Prime p₀= 458016100985738507 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 40 2 28 2 4 2 22 2 (?)
a_n: 0 2 42 44 84 86 114 116 120 122 144 146
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: 146
Found by: Cruncher Pete
db: batch=70, k=12, 40 40 28 4 22

SPT(14)	458015976018040163	0 78 80 84 126 140 150 164 174 188 230 234 236 314	-124967698344
SPT(16)	458015989942214731	0 10 30 40 42 100 136 156 196 216 252 310 312 322 342 352	-111043523776
SPT(14)	458016014391060457	0 22 96 156 166 216 252 280 316 366 376 436 510 532	-86594678050
SPT(14)	458016080687747357	0 6 20 24 80 86 90 140 144 150 206 210 224 230	-20297991150
SPT(14)	458016084365701969	0 18 22 24 28 52 72 100 120 144 148 150 154 172	-16620036538
SPT(14)	458016095746980101	0 6 30 42 60 66 86 162 182 188 206 218 242 248	-5238758406
SPT(14)	458016111015612421	0 6 28 42 82 126 130 138 142 186 226 240 262 268	10029873914
SPT(14)	458016117273434407	0 52 64 84 100 120 150 154 184 204 220 240 252 304	16287695900
SPT(14)	458016120009537731	0 36 50 80 116 132 146 162 176 192 228 258 272 308	19023799224
TPT(12)	458016131658608177	0 2 12 14 30 32 42 44 114 116 132 134	30672869670
SPT(14)	458016134155258379	0 2 12 38 54 122 152 210 240 308 324 350 360 362	33169519872