Prime p₀= 25893946116512939 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 34 2 82 2 16 2 40 2 (?)
a_n: 0 2 12 14 48 50 132 134 150 152 192 194
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: 194
Found by: Cruncher Pete
db: batch=65, k=12, 10 34 82 16 40

SPT(14)	25893919290013417	0 12 40 60 82 114 126 130 142 174 196 216 244 256	-26826499522
SPT(14)	25893929974629929	0 14 32 60 78 92 128 174 210 224 242 270 288 302	-16141883010
TPT(12)	25893932866528511	0 2 36 38 96 98 156 158 180 182 198 200	-13249984428
SPT(14)	25893939287802263	0 6 54 108 110 156 174 230 248 294 296 350 398 404	-6828710676
TPT(14)	25893942664604549	0 2 78 80 120 122 150 152 162 164 168 170 192 194	-3451908390
SPT(14)	25893946068362381	0 36 48 60 78 86 98 120 132 140 158 170 182 218	-48150558
SPT(14)	25893948413248337	0 6 14 30 32 44 56 90 102 114 116 132 140 146	2296735398
SPT(14)	25893954432515339	0 2 18 20 48 114 144 158 188 254 282 284 300 302	8316002400
SPT(14)	25893960255476387	0 2 32 42 54 86 144 182 240 272 284 294 324 326	14138963448
TPT(12)	25893972941711969	0 2 12 14 78 80 90 92 120 122 132 134	26825199030
SPT(14)	25893976400431483	0 10 58 60 66 78 94 120 136 148 154 156 204 214	30283918544