Prime p₀= 416051616353974619 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 4 2 148 2 28 2 10 2 (?)
a_n: 0 2 12 14 18 20 168 170 198 200 210 212
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: 212
Found by: Cruncher Pete
db: batch=70, k=12, 10 4 148 28 10

SPT(14)	416051512787771869	0 22 24 28 54 60 88 144 172 178 204 208 210 232	-103566202750
TPT(12)	416051523787505561	0 2 60 62 90 92 96 98 156 158 198 200	-92566469058
SPT(14)	416051535121446491	0 18 42 78 152 182 186 242 246 276 350 386 410 428	-81232528128
SPT(14)	416051548085614139	0 12 98 114 132 150 152 210 212 230 248 264 350 362	-68268360480
SPT(14)	416051557305111337	0 16 30 60 70 100 114 166 180 210 220 250 264 280	-59048863282
SPT(14)	416051560982384531	0 8 42 50 78 96 102 116 122 140 168 176 210 218	-55371590088
TPT(12)	416051633250055259	0 2 18 20 30 32 42 44 72 74 90 92	16896080640
SPT(14)	416051641746575749	0 10 18 22 24 28 48 124 144 148 150 154 162 172	25392601130
SPT(14)	416051641875127501	0 6 28 52 96 112 130 258 276 292 336 360 382 388	25521152882
SPT(14)	416051652637244609	0 14 20 68 72 90 98 144 152 170 174 222 228 242	36283269990
SPT(14)	416051653123833301	0 22 40 58 60 66 82 126 142 148 150 168 186 208	36769858682