Prime p₀= 416052555808406969 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 58 2 10 2 28 2 64 2 10 2 (?)
a_n: 0 2 60 62 72 74 102 104 168 170 180 182
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: 182
Found by: Cruncher Pete
db: batch=70, k=12, 58 10 28 64 10

SPT(14)	416052466602774679	0 60 72 90 112 168 174 178 184 240 262 280 292 352	-89205632290
SPT(14)	416052490204577311	0 16 42 66 82 88 112 126 150 156 172 196 222 238	-65603829658
SPT(14)	416052511640793353	0 8 14 54 170 204 210 254 260 294 410 450 456 464	-44167613616
SPT(14)	416052525125632903	0 6 18 36 40 54 118 126 190 204 208 226 238 244	-30682774066
SPT(14)	416052533641079207	0 20 32 56 66 90 116 126 152 176 186 210 222 242	-22167327762
SPT(14)	416052542367275017	0 36 54 72 114 142 154 222 234 262 304 322 340 376	-13441131952
SPT(14)	416052556209400697	0 14 30 66 74 200 224 252 276 402 410 446 462 476	400993728
SPT(20)	416052560274560333	0 24 50 80 98 104 126 144 146 204 230 288 290 308 330 336 354 384 410 434	4466153364
SPT(14)	416052562816827707	0 12 30 36 42 56 72 140 156 170 176 182 200 212	7008420738
SPT(14)	416052566435083283	0 18 26 56 60 68 98 156 186 194 198 228 236 254	10626676314
SPT(14)	416052574634100301	0 46 88 102 108 112 160 228 276 280 286 300 342 388	18825693332