Prime p₀= 400429696170379487 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 76 2 10 2 16 2 10 2 (?)
a_n: 0 2 42 44 120 122 132 134 150 152 162 164
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: Cruncher Pete
db: batch=70, k=12, 40 76 10 16 10

SPT(14)	400429666582187311	0 46 66 76 90 112 156 196 240 262 276 286 306 352	-29588192176
TPT(12)	400429673697669377	0 2 24 26 54 56 102 104 144 146 150 152	-22472710110
SPT(14)	400429681982616971	0 20 122 152 188 240 242 348 350 402 438 468 570 590	-14187762516
SPT(14)	400429687714416859	0 22 28 42 70 108 114 148 154 192 220 234 240 262	-8455962628
TPT(12)	400429688014335359	0 2 72 74 78 80 120 122 162 164 462 464	-8156044128
TPT(12)	400429694804645921	0 2 6 8 30 32 156 158 186 188 198 200	-1365733566
SPT(14)	400429729949971129	0 18 22 52 108 114 118 144 148 154 210 240 244 262	33779591642
TPT(12)	400429747011322331	0 2 78 80 90 92 198 200 240 242 246 248	50840942844
SPT(14)	400429756051179731	0 2 38 60 86 90 120 128 158 162 188 210 246 248	59880800244
SPT(14)	400429797997949623	0 18 96 124 144 150 156 178 184 190 210 238 316 334	101827570136
TPT(12)	400429821351384707	0 2 54 56 150 152 210 212 240 242 252 254	125181005220