Prime p₀= 673568320707995567 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 112 2 34 2 28 2 22 2 58 2 (?)
a_n: 0 2 114 116 150 152 180 182 204 206 264 266
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: 266
Found by: KAMCOBILL
db: batch=72, k=12, 112 34 28 22 58

SPT(16)	673568186274583357	0 4 36 70 72 114 120 142 174 196 202 244 246 280 312 316	-134433412210
TPT(12)	673568209547148569	0 2 12 14 168 170 210 212 222 224 258 260	-111160846998
SPT(16)	673568227449599887	0 12 42 82 100 130 144 192 202 250 264 294 312 352 382 394	-93258395680
TPT(12)	673568276651302691	0 2 138 140 156 158 168 170 180 182 198 200	-44056692876
STPT(10)	673568276651302829	0 2 18 20 30 32 42 44 60 62	-44056692738
TPT(12)	673568297650118207	0 2 42 44 72 74 120 122 162 164 192 194	-23057877360
TPT(12)	673568345294504477	0 2 54 56 102 104 114 116 180 182 270 272	24586508910
TPT(12)	673568345554753247	0 2 30 32 60 62 132 134 252 254 300 302	24846757680
SPT(16)	673568423856404749	0 18 54 60 82 84 100 124 168 192 208 210 232 238 274 292	103148409182
TPT(12)	673568481128139341	0 2 66 68 180 182 330 332 390 392 456 458	160420143774
TPT(12)	673568578750060757	0 2 84 86 150 152 162 164 234 236 252 254	258042065190