Prime p₀= 409808207919127079 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 4 2 40 2 76 2 28 2 (?)
a_n: 0 2 12 14 18 20 60 62 138 140 168 170
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: Daniel
db: batch=70, k=12, 10 4 40 76 28

SPT(14)	409808117297758031	0 2 90 108 116 150 156 182 188 222 230 248 336 338	-90621369048
SPT(14)	409808120019764077	0 22 24 36 66 94 132 184 222 250 280 292 294 316	-87899363002
SPT(14)	409808122304513039	0 30 50 90 92 98 120 260 282 288 290 330 350 380	-85614614040
TPT(12)	409808156968259837	0 2 30 32 72 74 84 86 102 104 132 134	-50950867242
SPT(14)	409808167171860607	0 22 40 42 120 124 132 184 192 196 274 276 294 316	-40747266472
TPT(12)	409808183345133869	0 2 90 92 162 164 228 230 282 284 312 314	-24573993210
SPT(14)	409808270397506947	0 22 24 40 72 150 184 192 226 304 336 352 354 376	62478379868
SPT(14)	409808270922259661	0 20 30 78 86 116 140 258 282 312 320 368 378 398	63003132582
SPT(14)	409808318308227719	0 48 72 90 132 138 144 168 174 180 222 240 264 312	110389100640
SPT(14)	409808320056758587	0 12 16 40 42 54 60 136 142 154 156 180 184 196	112137631508
SPT(14)	409808320070624269	0 4 12 70 72 88 144 208 264 280 282 340 348 352	112151497190