Prime p₀= 7438866700571357 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 76 2 40 2 46 2 40 2 (?)
a_n: 0 2 42 44 120 122 162 164 210 212 252 254
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: 254
Found by: crashtech
db: batch=62, k=12, 40 76 40 46 40

SPT(14)	7438823628055289	0 2 18 30 32 38 60 92 114 120 122 134 150 152	-43072516068
SPT(14)	7438823765934719	0 12 134 144 158 170 210 212 252 264 278 288 410 422	-42934636638
SPT(14)	7438830876351341	0 26 56 60 90 126 132 236 242 278 308 312 342 368	-35824220016
SPT(14)	7438848015029521	0 18 70 96 100 126 132 136 142 168 172 198 250 268	-18685541836
SPT(14)	7438850703988621	0 16 46 100 102 126 150 172 196 220 222 276 306 322	-15996582736
SPT(14)	7438856384001563	0 36 50 54 78 96 108 236 248 266 290 294 308 344	-10316569794
SPT(14)	7438873144541141	0 30 56 62 72 86 116 156 186 200 210 216 242 272	6443969784
SPT(14)	7438873578089339	0 60 72 110 140 152 210 254 312 324 354 392 404 464	6877517982
SPT(14)	7438883179614169	0 28 30 40 72 82 114 118 150 160 192 202 204 232	16479042812
SPT(14)	7438884238296733	0 6 10 34 84 118 120 124 126 160 210 234 238 244	17537725376
SPT(14)	7438904627421887	0 6 14 20 44 60 72 104 116 132 156 162 170 176	37926850530