Prime p₀= 400284064623335999 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 46 2 40 2 28 2 16 2 (?)
a_n: 0 2 30 32 78 80 120 122 150 152 168 170
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: desktop64
db: batch=70, k=12, 28 46 40 28 16

TPT(12)	400284030760295237	0 2 24 26 84 86 150 152 162 164 174 176	-33863040762
SPT(14)	400284036093931667	0 20 32 72 104 116 140 186 210 222 254 294 306 326	-28529404332
SPT(14)	400284039040515593	0 6 14 80 96 110 120 194 204 218 234 300 308 314	-25582820406
SPT(14)	400284048211981939	0 22 42 48 54 64 70 102 108 118 124 130 150 172	-16411354060
SPT(16)	400284050769758341	0 36 90 142 198 238 250 268 270 288 300 340 396 448 502 538	-13853577658
SPT(14)	400284055048508357	0 44 60 72 90 132 140 174 182 224 242 254 270 314	-9574827642
SPT(14)	400284072832833697	0 22 76 114 132 162 232 264 334 364 382 420 474 496	8209497698
SPT(14)	400284127573001131	0 40 78 88 106 130 150 208 228 252 270 280 318 358	62949665132
SPT(14)	400284135414882569	0 8 30 50 60 68 74 198 204 212 222 242 264 272	70791546570
TPT(12)	400284136160345537	0 2 90 92 102 104 144 146 300 302 312 314	71537009538
SPT(14)	400284179075439319	0 22 42 72 90 118 124 198 204 232 250 280 300 322	114452103320