Prime p₀= 51033600578857649 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 208 2 28 2 10 2 4 2 22 2 (?)
a_n: 0 2 210 212 240 242 252 254 258 260 282 284
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: Dario666
db: batch=65, k=12, 208 28 10 4 22

SPT(14)	51033574951683157	0 10 12 54 60 70 120 214 264 274 280 322 324 334	-25627174492
SPT(14)	51033575996617189	0 10 24 30 94 100 120 154 174 180 244 250 264 274	-24582240460
SPT(14)	51033583416099073	0 4 70 84 100 124 136 228 240 264 280 294 360 364	-17162758576
TPT(12)	51033592317287339	0 2 60 62 90 92 102 104 138 140 210 212	-8261570310
SPT(14)	51033597922957513	0 28 34 36 90 100 108 166 174 184 238 240 246 274	-2655900136
SPT(14)	51033600322128817	0 40 66 112 120 144 154 162 172 196 204 250 276 316	-256728832
SPT(14)	51033614225148739	0 10 28 52 84 174 198 214 238 328 360 384 402 412	13646291090
SPT(14)	51033631353596609	0 2 18 72 102 120 144 158 182 200 230 284 300 302	30774738960
TPT(12)	51033644568033509	0 2 258 260 492 494 522 524 588 590 618 620	43989175860
STPT(10)	51033666706977431	0 2 36 38 78 80 120 122 156 158	66128119782
SPT(14)	51033669856812737	0 30 72 146 152 156 162 224 230 234 240 314 356 386	69277955088