Prime p₀= 347199941665944539 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 4 2 190 2 16 2 22 2 (?)
a_n: 0 2 12 14 18 20 210 212 228 230 252 254
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: 254
Found by: Cruncher Pete
db: batch=70, k=12, 10 4 190 16 22

SPT(14)	347199923799585977	0 2 30 60 72 102 116 120 134 164 176 206 234 236	-17866358562
SPT(14)	347199925269588133	0 64 88 100 130 150 156 178 184 204 234 246 270 334	-16396356406
STPT(10)	347199925548633887	0 2 30 32 120 122 210 212 240 242	-16117310652
TPT(12)	347199931579306229	0 2 12 14 72 74 180 182 270 272 312 314	-10086638310
TPT(12)	347199933621089447	0 2 42 44 54 56 150 152 162 164 222 224	-8044855092
SPT(14)	347199935821275811	0 28 30 46 58 72 82 126 136 150 162 178 180 208	-5844668728
SPT(14)	347199954245511509	0 42 50 60 74 108 114 128 134 168 182 192 200 242	12579566970
SPT(14)	347199970492974581	0 2 8 68 78 86 152 156 222 230 240 300 306 308	28827030042
SPT(14)	347199979475290001	0 2 32 42 78 86 90 128 132 140 176 186 216 218	37809345462
SPT(14)	347199979996818349	0 10 24 30 34 48 58 120 130 144 148 154 168 178	38330873810
SPT(14)	347199980371461067	0 12 22 34 60 112 126 160 174 226 252 264 274 286	38705516528