Prime p₀= 471679448805108827 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 130 2 70 2 58 2 106 2 40 2 (?)
a_n: 0 2 132 134 204 206 264 266 372 374 414 416
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: 416
Found by: Cruncher Pete
db: batch=70, k=12, 130 70 58 106 40

SPT(16)	471679376388299777	0 24 90 144 150 162 164 194 300 330 332 344 350 404 470 494	-72416809050
SPT(14)	471679379141504153	0 6 14 50 146 168 176 228 236 258 354 390 398 404	-69663604674
SPT(14)	471679413339610241	0 6 12 36 42 68 98 120 150 176 182 206 212 218	-35465498586
SPT(16)	471679418065254499	0 58 100 102 114 162 172 184 198 210 220 268 280 282 324 382	-30739854328
SPT(14)	471679430034716947	0 36 40 112 130 154 186 190 222 246 264 336 340 376	-18770391880
TPT(14)	471679446575537591	0 2 96 98 156 158 180 182 198 200 210 212 228 230	-2229571236
SPT(14)	471679465519004089	0 28 34 42 48 70 84 88 102 124 130 138 144 172	16713895262
SPT(14)	471679484287530763	0 28 34 40 58 66 88 96 118 126 144 150 156 184	35482421936
SPT(14)	471679498620374489	0 30 32 60 144 158 210 212 264 278 362 390 392 422	49815265662
SPT(14)	471679523786931611	0 8 12 72 78 90 110 120 140 152 158 218 222 230	74981822784
SPT(14)	471679547760199399	0 22 24 64 70 132 180 232 280 342 348 388 390 412	98955090572