Prime p₀= 290586604635179471 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 34 2 28 2 58 2 22 2 16 2 (?)
a_n: 0 2 36 38 66 68 126 128 150 152 168 170
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: Paul
db: batch=69, k=12, 34 28 58 22 16

SPT(14)	290586518205124109	0 12 24 42 44 90 134 168 212 258 260 278 290 302	-86430055362
SPT(14)	290586522941928023	0 44 74 126 156 200 206 258 264 308 338 390 420 464	-81693251448
SPT(14)	290586544974227239	0 22 40 48 64 82 108 124 150 168 184 192 210 232	-59660952232
SPT(14)	290586561762759967	0 12 42 66 124 136 172 174 210 222 280 304 334 346	-42872419504
SPT(16)	290586583306829021	0 18 42 62 72 90 108 170 270 332 350 368 378 398 422 440	-21328350450
SPT(14)	290586604566991591	0 36 42 70 82 96 102 130 136 150 162 190 196 232	-68187880
TPT(12)	290586631450559369	0 2 30 32 48 50 90 92 102 104 132 134	26815379898
SPT(14)	290586633512871347	0 12 14 42 60 80 92 144 156 176 194 222 224 236	28877691876
SPT(14)	290586640649748007	0 34 42 52 64 70 94 102 126 132 144 154 162 196	36014568536
SPT(14)	290586667067924141	0 62 78 80 98 132 146 162 176 210 228 230 246 308	62432744670
SPT(14)	290586671516464991	0 2 92 120 122 128 152 318 342 348 350 378 468 470	66881285520