Prime p₀= 278882372377131371 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 34 2 52 2 28 2 46 2 16 2 (?)
a_n: 0 2 36 38 90 92 120 122 168 170 186 188
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: 188
Found by: [AF>Amis des Lapins] Ceclo
db: batch=69, k=12, 34 52 28 46 16

SPT(16)	278882314129005113	0 38 48 66 80 140 168 176 198 206 234 294 308 326 336 374	-58248126258
TPT(12)	278882342965328411	0 2 36 38 78 80 126 128 240 242 246 248	-29411802960
SPT(14)	278882343486064553	0 36 78 96 114 134 138 176 180 200 218 236 278 314	-28891066818
STPT(10)	278882353114814717	0 2 30 32 72 74 114 116 144 146	-19262316654
SPT(14)	278882366911406663	0 54 96 108 138 140 170 264 294 296 326 338 380 434	-5465724708
SPT(14)	278882371955026003	0 24 76 90 94 118 120 154 156 180 184 198 250 274	-422105368
SPT(14)	278882379557687041	0 6 28 30 36 58 66 82 90 112 118 120 142 148	7180555670
SPT(14)	278882385272179121	0 6 86 96 108 116 138 158 180 188 200 210 290 296	12895047750
SPT(14)	278882388218858239	0 28 30 72 88 118 160 180 222 252 268 310 312 340	15841726868
SPT(14)	278882393594924837	0 44 72 84 120 146 170 216 240 266 302 314 342 386	21217793466
SPT(14)	278882405414698847	0 6 54 60 62 116 132 164 180 234 236 242 290 296	33037567476