Prime p₀= 338913255966370847 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 34 2 40 2 46 2 28 2 (?)
a_n: 0 2 24 26 60 62 102 104 150 152 180 182
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: 182
Found by: Cruncher Pete
db: batch=70, k=12, 22 34 40 46 28

SPT(14)	338913201462282703	0 58 64 70 78 88 130 138 180 190 198 204 210 268	-54504088144
SPT(14)	338913201814203479	0 2 30 50 72 78 84 128 134 140 162 182 210 212	-54152167368
SPT(16)	338913202708195741	0 6 30 40 70 72 82 90 118 126 136 138 168 178 202 208	-53258175106
SPT(14)	338913223215067549	0 12 52 124 130 142 168 184 210 222 228 300 340 352	-32751303298
SPT(14)	338913243974837813	0 14 54 98 120 156 164 210 218 254 276 320 360 374	-11991533034
SPT(14)	338913249286608457	0 4 10 24 40 54 60 76 82 96 112 126 132 136	-6679762390
SPT(14)	338913279999972673	0 10 28 34 64 78 84 94 100 114 144 150 168 178	24033601826
SPT(14)	338913285577779751	0 10 16 40 42 66 70 72 76 100 102 126 132 142	29611408904
SPT(14)	338913292754138129	0 18 24 48 54 224 228 230 234 404 410 434 440 458	36787767282
SPT(14)	338913307472055367	0 6 76 100 126 132 156 160 184 190 216 240 310 316	51505684520
TPT(12)	338913328145362301	0 2 6 8 48 50 156 158 198 200 336 338	72178991454