Prime p₀= 441153945628332449 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 10 2 58 2 58 2 4 2 (?)
a_n: 0 2 30 32 42 44 102 104 162 164 168 170
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: Cruncher Pete
db: batch=70, k=12, 28 10 58 58 4

SPT(14)	441153868631589983	0 36 56 78 140 168 216 260 308 336 398 420 440 476	-76996742466
SPT(14)	441153874605597497	0 36 42 50 102 114 122 204 212 224 276 284 290 326	-71022734952
SPT(16)	441153892200918487	0 16 30 52 84 114 120 142 204 226 232 262 294 316 330 346	-53427413962
SPT(14)	441153925059974197	0 4 30 52 60 70 84 130 144 154 162 184 210 214	-20568358252
SPT(14)	441153937464375461	0 2 42 50 120 132 152 156 176 188 258 266 306 308	-8163956988
SPT(14)	441153943314301709	0 24 60 72 90 104 162 170 228 242 260 272 308 332	-2314030740
SPT(14)	441153947922917521	0 36 70 78 88 90 118 138 166 168 178 186 220 256	2294585072
TPT(12)	441153953376446741	0 2 60 62 138 140 156 158 168 170 198 200	7748114292
SPT(14)	441153979584873619	0 22 42 78 100 108 150 190 232 240 262 298 318 340	33956541170
SPT(14)	441153997788224551	0 10 46 48 78 150 190 216 256 328 358 360 396 406	52159892102
SPT(14)	441154055404314937	0 16 34 42 60 76 112 144 180 196 214 222 240 256	109775982488