Prime p₀= 259595321149555799 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 166 2 238 2 28 2 22 2 16 2 (?)
a_n: 0 2 168 170 408 410 438 440 462 464 480 482
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: 482
Found by: desktop64
db: batch=69, k=12, 166 238 28 22 16

SPT(14)	259595275106160401	0 18 20 62 78 92 102 116 126 140 156 198 200 218	-46043395398
SPT(14)	259595299172935301	0 8 20 42 72 92 132 206 246 266 296 318 330 338	-21976620498
SPT(14)	259595305873371931	0 28 82 106 108 112 168 220 276 280 282 306 360 388	-15276183868
SPT(14)	259595310207956057	0 12 14 32 54 96 144 152 200 242 264 282 284 296	-10941599742
TPT(12)	259595314387632467	0 2 12 14 24 26 30 32 54 56 72 74	-6761923332
TPT(12)	259595315672368769	0 2 60 62 78 80 168 170 240 242 300 302	-5477187030
SPT(14)	259595324201968549	0 18 72 114 132 144 204 208 268 280 298 340 394 412	3052412750
SPT(14)	259595327974652569	0 4 30 34 40 48 70 132 154 162 168 172 198 202	6825096770
TPT(12)	259595330542399301	0 2 6 8 30 32 60 62 126 128 156 158	9392843502
SPT(14)	259595342663375981	0 6 20 56 62 80 92 96 108 126 132 168 182 188	21513820182
SPT(16)	259595353270334593	0 36 40 46 70 78 96 124 150 178 196 204 228 234 238 274	32120778794