Prime p₀= 1299477194031316799 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 4 2 22 2 4 2 40 2 (?)
a_n: 0 2 42 44 48 50 72 74 78 80 120 122
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: 122
Found by: Cruncher Pete
db: batch=77, k=12, 2 40 2 4 2 22

SPT(16)	1299475548012667733	0 8 30 66 80 120 164 186 218 240 284 324 338 374 396 404	-1646018649066
SPT(16)	1299475842524298697	0 4 24 52 60 66 136 180 256 300 370 376 384 412 432 436	-1351507018102
STPT(10)	1299476221855242659	0 2 48 50 90 92 132 134 180 182	-972176074140
SPT(16)	1299476381584994783	0 30 86 144 146 150 174 186 188 200 224 228 230 288 344 374	-812446322016
SPT(16)	1299476503804653571	0 28 48 106 126 138 148 150 178 180 190 202 222 280 300 328	-690226663228
TPT(14)	1299477007353080531	0 2 6 8 48 50 66 68 96 98 120 122 138 140	-186678236268
SPT(16)	1299477454943829769	0 90 114 132 138 180 192 222 280 310 322 364 370 388 412 502	260912512970
STPT(10)	1299477960078751931	0 2 30 32 78 80 126 128 156 158	766047435132
SPT(16)	1299477975711880609	0 10 28 30 52 58 64 82 210 228 234 240 262 264 282 292	781680563810
SPT(16)	1299478054278286903	0 4 30 100 126 138 186 196 198 208 256 268 294 364 390 394	860246970104
STPT(10)	1299478092174644279	0 2 18 20 60 62 102 104 120 122	898143327480