Prime p₀= 588771604113579617 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 64 2 28 2 28 2 10 2 (?)
a_n: 0 2 24 26 90 92 120 122 150 152 162 164
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: 164
Found by: Dr Who Fan
db: batch=71, k=12, 22 64 28 28 10

SPT(14)	588771548056128043	0 6 34 60 126 136 168 346 378 388 454 480 508 514	-56057451574
SPT(14)	588771558038594251	0 10 18 70 96 118 132 136 150 172 198 250 258 268	-46074985366
TPT(12)	588771559034268521	0 2 18 20 30 32 36 38 156 158 168 170	-45079311096
SPT(14)	588771572986488077	0 30 42 50 72 132 156 200 224 284 306 314 326 356	-31127091540
TPT(12)	588771573653850239	0 2 72 74 102 104 120 122 240 242 288 290	-30459729378
SPT(14)	588771575186592593	0 20 38 50 66 78 90 134 146 158 174 186 204 224	-28926987024
SPT(14)	588771616876226011	0 12 22 40 78 90 112 126 148 160 198 216 226 238	12762646394
SPT(14)	588771647234973451	0 6 40 42 78 90 130 198 238 250 286 288 322 328	43121393834
SPT(14)	588771648782637037	0 4 6 16 54 60 70 90 100 106 144 154 156 160	44669057420
TPT(12)	588771667254214511	0 2 18 20 90 92 156 158 168 170 198 200	63140634894
SPT(14)	588771673285609309	0 18 34 40 84 94 124 144 174 184 228 234 250 268	69172029692