Prime p₀= 376889815820879927 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 52 2 88 2 4 2 40 2 88 2 (?)
a_n: 0 2 54 56 144 146 150 152 192 194 282 284
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: 284
Found by: Cruncher Pete
db: batch=70, k=12, 52 88 4 40 88

SPT(14)	376889728497508117	0 16 36 64 72 82 84 112 114 124 132 160 180 196	-87323371810
SPT(14)	376889745926728381	0 12 18 36 88 96 102 106 112 120 172 190 196 208	-69894151546
SPT(14)	376889767805112433	0 4 54 204 258 264 268 270 274 280 334 484 534 538	-48015767494
SPT(14)	376889777904854309	0 12 50 54 90 104 128 144 168 182 218 222 260 272	-37916025618
SPT(14)	376889801910083543	0 8 30 110 116 126 138 176 188 198 204 284 306 314	-13910796384
TPT(12)	376889808511410449	0 2 78 80 90 92 132 134 162 164 222 224	-7309469478
SPT(14)	376889846551590583	0 16 58 78 84 96 148 156 208 220 226 246 288 304	30730710656
SPT(20)	376889858243907223	0 10 28 34 124 216 246 274 300 304 330 334 360 388 418 510 600 606 624 634	42423027296
SPT(14)	376889860640585821	0 22 36 126 162 190 202 216 228 256 292 382 396 418	44819705894
SPT(14)	376889862498445783	0 6 34 40 78 90 100 144 154 166 204 210 238 244	46677565856
TPT(12)	376889876134643099	0 2 18 20 42 44 48 50 72 74 90 92	60313763172