Prime p₀= 78278774610099311 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 46 2 46 2 10 2 28 2 10 2 (?)
a_n: 0 2 48 50 96 98 108 110 138 140 150 152
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: 152
Found by: emoga
db: batch=67, k=12, 46 46 10 28 10

TPT(12)	78278702776224659	0 2 18 20 42 44 78 80 90 92 102 104	-71833874652
SPT(14)	78278728466645101	0 28 36 42 52 58 70 108 120 126 136 142 150 178	-46143454210
TPT(12)	78278737916700611	0 2 78 80 90 92 96 98 120 122 180 182	-36693398700
SPT(14)	78278749777236623	0 26 30 80 96 98 140 156 198 200 216 266 270 296	-24832862688
SPT(14)	78278763525939859	0 4 12 42 54 60 64 78 82 88 100 130 138 142	-11084159452
SPT(14)	78278767796362883	0 8 44 50 78 84 114 164 194 200 228 234 270 278	-6813736428
SPT(14)	78278775155323123	0 10 30 58 106 108 124 150 166 168 216 244 264 274	545223812
SPT(14)	78278781644430319	0 30 42 78 94 130 138 154 162 198 214 250 262 292	7034331008
SPT(14)	78278785736020171	0 18 46 52 60 66 96 112 142 148 156 162 190 208	11125920860
SPT(14)	78278800750542409	0 78 90 94 138 154 160 168 174 190 234 238 250 328	26140443098
SPT(14)	78278803434401149	0 28 30 60 90 138 144 154 160 208 238 268 270 298	28824301838