Prime p₀= 278648360139037241 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 4 2 70 2 58 2 10 2 16 2 (?)
a_n: 0 2 6 8 78 80 138 140 150 152 168 170
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: 170
Found by: [AF>Amis des Lapins] Ceclo
db: batch=69, k=12, 4 70 58 10 16

SPT(14)	278648220049674703	0 16 46 78 88 120 130 144 154 186 196 228 258 274	-140089362538
SPT(14)	278648245579882921	0 18 52 66 70 78 96 112 130 138 142 156 190 208	-114559154320
SPT(14)	278648282088517051	0 12 16 22 40 42 46 72 76 78 96 102 106 118	-78050520190
TPT(12)	278648282916743939	0 2 12 14 78 80 90 92 168 170 180 182	-77222293302
SPT(16)	278648303121555259	0 34 72 112 162 168 184 190 222 228 244 250 300 340 378 412	-57017481982
SPT(14)	278648310222696707	0 2 20 30 44 126 144 182 200 282 296 306 324 326	-49916340534
SPT(14)	278648369167636723	0 24 34 36 76 90 106 138 154 168 208 210 220 244	9028599482
SPT(14)	278648389796483537	0 20 32 36 74 140 180 266 306 372 410 414 426 446	29657446296
SPT(14)	278648426727529591	0 18 52 102 108 130 166 222 258 280 286 336 370 388	66588492350
TPT(12)	278648431616378741	0 2 66 68 108 110 156 158 168 170 240 242	71477341500
TPT(12)	278648447894338979	0 2 72 74 78 80 132 134 198 200 240 242	87755301738