Prime p₀= 349548656118767381 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 4 2 58 2 10 2 10 2 34 2 (?)
a_n: 0 2 6 8 66 68 78 80 90 92 126 128
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: 128
Found by: paulteo
db: batch=70, k=12, 4 58 10 10 34

SPT(14)	349548563737863901	0 10 48 60 132 138 178 210 250 256 328 340 378 388	-92380903480
SPT(14)	349548578005649137	0 10 64 70 120 124 136 150 162 166 216 222 276 286	-78113118244
SPT(14)	349548603576671743	0 46 54 70 88 96 100 114 118 126 144 160 168 214	-52542095638
SPT(14)	349548618655734629	0 24 50 60 62 102 104 138 140 180 182 192 218 242	-37463032752
SPT(14)	349548642616751101	0 28 30 40 42 52 88 150 186 196 198 208 210 238	-13502016280
SPT(14)	349548647474110873	0 10 24 40 76 136 196 228 288 348 384 400 414 424	-8644656508
SPT(14)	349548669450588523	0 10 28 58 70 88 108 136 156 174 186 216 234 244	13331821142
SPT(14)	349548684455194577	0 14 20 86 90 110 114 146 150 170 174 240 246 260	28336427196
SPT(14)	349548689366986541	0 12 50 60 80 92 126 176 210 222 242 252 290 302	33248219160
SPT(14)	349548695879870587	0 24 34 42 60 70 90 214 234 244 262 270 280 304	39761103206
SPT(14)	349548711858952939	0 42 48 58 72 82 84 88 90 100 114 124 130 172	55740185558