Prime p₀= 375588358368054581 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 76 2 40 2 16 2 16 2 10 2 (?)
a_n: 0 2 78 80 120 122 138 140 156 158 168 170
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: 170
Found by: nenym
db: batch=70, k=12, 76 40 16 16 10

SPT(14)	375588254526548333	0 8 74 90 96 98 138 266 306 308 314 330 396 404	-103841506248
SPT(16)	375588309651141673	0 34 100 118 168 196 198 238 276 316 318 346 396 414 480 514	-48716912908
SPT(16)	375588309660399467	0 2 80 86 120 156 224 230 276 282 350 386 420 426 504 506	-48707655114
SPT(14)	375588309784456733	0 6 18 26 60 96 104 150 158 194 228 236 248 254	-48583597848
SPT(14)	375588347033827621	0 22 30 40 78 150 156 232 238 310 348 358 366 388	-11334226960
SPT(14)	375588347434941259	0 22 42 58 132 142 154 168 180 190 264 280 300 322	-10933113322
TPT(12)	375588398477807267	0 2 42 44 54 56 210 212 240 242 282 284	40109752686
SPT(14)	375588437593475567	0 74 80 84 90 116 126 170 180 206 212 216 222 296	79225420986
SPT(14)	375588482667023099	0 42 102 104 144 180 182 402 404 440 480 482 542 584	124298968518
SPT(20)	375588482671196843	0 54 114 144 158 168 170 180 188 230 234 276 284 294 296 306 320 350 410 464	124303142262
SPT(14)	375588485559989753	0 20 50 86 90 104 108 146 150 164 168 204 234 254	127191935172