Prime p₀= 23181635966504591 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 4 2 22 2 4 2 40 2 88 2 (?)
a_n: 0 2 6 8 30 32 36 38 78 80 168 170
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: Farscape
db: batch=65, k=12, 4 22 4 40 88

SPT(14)	23181589414475881	0 12 36 42 46 82 102 190 210 246 250 256 280 292	-46552028710
SPT(14)	23181595057134001	0 10 48 52 88 90 102 196 208 210 246 250 288 298	-40909370590
SPT(16)	23181596575185403	0 24 28 54 60 84 90 94 120 124 130 154 160 186 190 214	-39391319188
SPT(14)	23181604388280407	0 6 14 20 56 60 146 180 266 270 306 312 320 326	-31578224184
SPT(14)	23181617027400319	0 28 34 54 64 88 90 118 120 144 154 174 180 208	-18939104272
SPT(14)	23181631947595501	0 48 58 70 78 100 108 112 120 142 150 162 172 220	-4018909090
SPT(14)	23181640067429951	0 32 72 78 92 98 116 132 150 156 170 176 216 248	4100925360
TPT(12)	23181651131521607	0 2 60 62 84 86 90 92 102 104 114 116	15165017016
SPT(14)	23181653351776457	0 32 42 84 90 104 152 312 360 374 380 422 432 464	17385271866
SPT(14)	23181674205397387	0 4 72 106 114 166 186 250 270 322 330 364 432 436	38238892796
SPT(14)	23181676924043663	0 18 20 26 50 68 116 120 168 186 210 216 218 236	40957539072