Prime p₀= 77744200633056467 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 16 2 28 2 28 2 148 2 (?)
a_n: 0 2 24 26 42 44 72 74 102 104 252 254
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: Alez
db: batch=67, k=12, 22 16 28 28 148

SPT(14)	77744124033516653	0 6 20 30 66 86 168 188 270 290 326 336 350 356	-76599539814
SPT(14)	77744144305292767	0 30 46 54 60 96 154 156 214 250 256 264 280 310	-56327763700
SPT(14)	77744156991275981	0 42 90 108 120 150 162 176 188 218 230 248 296 338	-43641780486
SPT(16)	77744158283115703	0 18 36 54 84 106 124 130 144 150 168 190 220 238 256 274	-42349940764
SPT(20)	77744166975959581	0 18 30 42 48 76 82 96 100 108 160 168 172 186 192 220 226 238 250 268	-33657096886
SPT(14)	77744177882674139	0 48 68 78 92 104 110 162 168 180 194 204 224 272	-22750382328
SPT(14)	77744227730903827	0 46 52 64 90 106 136 210 240 256 282 294 300 346	27097847360
SPT(14)	77744230935651479	0 8 24 30 50 92 198 224 330 372 392 398 414 422	30302595012
SPT(14)	77744235390241781	0 32 60 98 116 126 138 140 152 162 180 218 246 278	34757185314
SPT(14)	77744257502032603	0 30 58 94 126 144 180 214 250 268 300 336 364 394	56868976136
SPT(14)	77744280098221787	0 32 56 74 92 134 144 152 162 204 222 240 264 296	79465165320