Prime p₀= 14032875578650457 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 28 2 196 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 240 242 270 272 282 284
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: crashtech
db: batch=62, k=12, 10 28 196 28 10

SPT(14)	14032848284663977	0 4 40 46 60 70 84 112 126 136 150 156 192 196	-27293986480
SPT(14)	14032852952041333	0 48 54 130 156 166 186 268 288 298 324 400 406 454	-22626609124
SPT(14)	14032854588549067	0 6 60 82 90 94 102 154 162 166 174 196 250 256	-20990101390
SPT(14)	14032866079235629	0 22 28 40 48 52 70 90 108 112 120 132 138 160	-9499414828
SPT(14)	14032869994526611	0 16 46 48 100 132 138 160 166 198 250 252 282 298	-5584123846
SPT(14)	14032873971182779	0 4 52 82 84 130 154 168 192 238 240 270 318 322	-1607467678
STPT(12)	14032875578650457	0 2 12 14 42 44 240 242 270 272 282 284	0
SPT(14)	14032896312995099	0 8 18 24 38 44 74 78 108 114 128 134 144 152	20734344642
SPT(14)	14032912394384111	0 20 26 56 62 72 116 126 170 180 186 216 222 242	36815733654
TPT(12)	14032920562655717	0 2 72 74 240 242 294 296 312 314 324 326	44984005260
SPT(14)	14032930796688577	0 22 46 72 82 100 112 114 126 144 154 180 204 226	55218038120