Prime p₀= 11317542384466697 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 52 2 136 2 46 2 10 2 10 2 (?)
a_n: 0 2 54 56 192 194 240 242 252 254 264 266
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: 266
Found by: Scortch
db: batch=62, k=12, 52 136 46 10 10

TPT(12)	11317494651430967	0 2 60 62 72 74 84 86 240 242 264 266	-47733035730
SPT(14)	11317495999543597	0 6 12 42 136 142 166 210 234 240 334 364 370 376	-46384923100
SPT(14)	11317502087004391	0 40 42 70 78 148 160 180 192 262 270 298 300 340	-40297462306
SPT(14)	11317513024858189	0 30 42 52 84 94 142 162 210 220 252 262 274 304	-29359608508
TPT(12)	11317525289166137	0 2 42 44 60 62 150 152 252 254 312 314	-17095300560
SPT(14)	11317532567385619	0 22 40 42 58 60 64 78 82 84 100 102 120 142	-9817081078
SPT(14)	11317551165668689	0 12 30 40 54 90 100 144 154 190 204 214 232 244	8781201992
SPT(14)	11317561082457559	0 4 12 24 28 40 70 72 102 114 118 130 138 142	18697990862
SPT(20)	11317568019362809	0 22 40 42 58 112 124 142 154 172 180 198 210 228 240 294 310 312 330 352	25634896112
SPT(14)	11317571145360511	0 6 12 30 42 48 52 96 100 106 118 136 142 148	28760893814
SPT(14)	11317573436105983	0 4 16 18 46 70 118 156 204 228 256 258 270 274	31051639286