Prime p₀= 2540335189868393507 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 40 2 28 2 40 2 28 2 (?)
a_n: 0 2 30 32 72 74 102 104 144 146 174 176
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: 176
Found by: Paul
db: batch=82, k=12, 2 28 2 40 2 28

STPT(10)	2540334091111735277	0 2 60 62 72 74 84 86 144 146	-1098756658230
STPT(10)	2540334410099916041	0 2 66 68 108 110 150 152 216 218	-779768477466
SPT(16)	2540334526019975119	0 64 100 114 138 162 238 250 252 264 340 364 388 402 438 502	-663848418388
SPT(16)	2540334683982781727	0 6 30 32 62 86 90 126 200 236 240 264 294 296 320 326	-505885611780
SPT(16)	2540334721416324769	0 60 84 88 100 124 154 160 192 198 228 252 264 268 292 352	-468452068738
STPT(10)	2540334874539991157	0 2 30 32 72 74 114 116 144 146	-315328402350
SPT(16)	2540335235904641899	0 12 72 120 124 142 168 258 274 364 390 408 412 460 520 532	46036248392
STPT(10)	2540335336982674067	0 2 42 44 72 74 102 104 144 146	147114280560
SPT(16)	2540335359438214183	0 6 10 18 28 48 70 94 150 174 196 216 226 234 238 244	169569820676
SPT(16)	2540335578418704361	0 16 18 40 42 70 72 88 120 136 138 166 168 190 192 208	388550310854
TPT(14)	2540336405041363337	0 2 54 56 162 164 222 224 264 266 390 392 402 404	1215172969830