Prime p₀= 404886809859872567 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 40 2 76 2 70 2 88 2 (?)
a_n: 0 2 12 14 54 56 132 134 204 206 294 296
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: 296
Found by: Cruncher Pete
db: batch=70, k=12, 10 40 76 70 88

SPT(14)	404886732925719389	0 8 14 30 38 48 80 132 164 174 182 198 204 212	-76934153178
SPT(14)	404886734615778377	0 14 50 72 84 114 152 162 200 230 242 264 300 314	-75244094190
SPT(14)	404886748389296837	0 20 56 72 80 144 174 182 212 276 284 300 336 356	-61470575730
TPT(12)	404886754394631329	0 2 30 32 132 134 162 164 198 200 210 212	-55465241238
SPT(14)	404886755273987797	0 30 40 72 90 94 100 126 132 136 154 186 196 226	-54585884770
TPT(12)	404886777005644277	0 2 12 14 24 26 42 44 54 56 180 182	-32854228290
TPT(12)	404886811910833379	0 2 12 14 78 80 108 110 150 152 162 164	2050960812
SPT(14)	404886841405558093	0 54 64 84 88 126 154 240 268 306 310 330 340 394	31545685526
SPT(14)	404886845281131439	0 24 30 78 90 118 120 142 144 172 184 232 238 262	35421258872
SPT(14)	404886845962616629	0 28 148 198 204 264 294 388 418 478 484 534 654 682	36102744062
SPT(14)	404886852597163621	0 6 60 72 76 126 132 136 142 192 196 208 262 268	42737291054