Prime p₀= 181517743256000729 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 4 2 82 2 4 2 130 2 (?)
a_n: 0 2 42 44 48 50 132 134 138 140 270 272
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: 272
Found by: desktop64
db: batch=69, k=12, 40 4 82 4 130

SPT(14)	181517643265682827	0 34 42 46 54 64 76 90 102 112 120 124 132 166	-99990317902
SPT(14)	181517649859440913	0 6 36 124 154 166 198 256 288 300 330 418 448 454	-93396559816
SPT(16)	181517672635345373	0 6 20 78 90 110 116 138 188 210 216 236 248 306 320 326	-70620655356
SPT(14)	181517702022452863	0 18 28 40 46 90 96 160 166 210 216 228 238 256	-41233547866
SPT(14)	181517711458831339	0 18 54 72 78 82 100 102 120 124 130 148 184 202	-31797169390
SPT(14)	181517717972665507	0 6 34 42 70 82 102 124 144 156 184 192 220 226	-25283335222
SPT(14)	181517746889019677	0 66 86 90 92 104 126 170 192 204 206 210 230 296	3633018948
TPT(12)	181517762007277517	0 2 54 56 84 86 90 92 120 122 150 152	18751276788
SPT(14)	181517766275023303	0 28 34 46 58 90 100 114 124 156 168 180 186 214	23019022574
SPT(14)	181517769980545781	0 12 32 68 102 110 122 168 180 188 222 258 278 290	26724545052
TPT(12)	181517775469885037	0 2 84 86 150 152 162 164 204 206 294 296	32213884308