Prime p₀= 27648642373187159 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 58 2 58 2 64 2 52 2 (?)
a_n: 0 2 42 44 102 104 162 164 228 230 282 284
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: 284
Found by: UBT - Timbo
db: batch=65, k=12, 40 58 58 64 52

SPT(14)	27648617355134077	0 24 46 84 100 106 126 130 150 156 172 210 232 256	-25018053082
SPT(14)	27648620642093237	0 44 86 90 120 122 140 156 174 176 206 210 252 296	-21731093922
SPT(14)	27648624821857471	0 22 42 78 112 130 148 150 168 186 220 256 276 298	-17551329688
SPT(14)	27648630157143773	0 24 44 66 78 84 86 108 110 116 128 150 170 194	-12216043386
TPT(12)	27648630622676339	0 2 48 50 258 260 300 302 342 344 378 380	-11750510820
SPT(14)	27648635147792089	0 22 54 72 84 100 112 132 144 160 172 190 222 244	-7225395070
SPT(14)	27648652998995761	0 10 36 46 66 78 222 286 430 442 462 472 498 508	10625808602
SPT(14)	27648669202117273	0 34 48 58 70 114 148 156 190 234 246 256 270 304	26828930114
SPT(14)	27648670561392719	0 12 14 20 42 60 62 102 104 122 144 150 152 164	28188205560
SPT(14)	27648670942912121	0 18 20 36 56 60 68 78 86 90 110 126 128 146	28569724962
SPT(14)	27648678586004207	0 20 30 84 116 134 176 180 222 240 272 326 336 356	36212817048