Prime p₀= 390592120650620039 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 28 2 76 2 130 2 40 2 (?)
a_n: 0 2 30 32 60 62 138 140 270 272 312 314
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: 314
Found by: desktop64
db: batch=70, k=12, 28 28 76 130 40

SPT(14)	390592051831816291	0 22 28 42 70 72 142 156 226 228 256 270 276 298	-68818803748
SPT(14)	390592057353963533	0 6 14 24 50 84 90 110 116 150 176 186 194 200	-63296656506
SPT(14)	390592062330757141	0 46 66 70 72 78 100 108 130 136 138 142 162 208	-58319862898
SPT(14)	390592085853376087	0 42 72 90 154 160 192 202 234 240 304 322 352 394	-34797243952
SPT(14)	390592113351788423	0 8 54 56 78 80 108 206 234 236 258 260 306 314	-7298831616
SPT(14)	390592118578204919	0 18 50 78 80 84 104 138 158 162 164 192 224 242	-2072415120
SPT(14)	390592132181935891	0 12 28 48 102 138 162 208 232 268 322 342 358 370	11531315852
SPT(14)	390592157096515909	0 22 40 64 78 94 112 150 168 184 198 222 240 262	36445895870
SPT(14)	390592173066200681	0 36 38 66 80 92 102 146 156 168 182 210 212 248	52415580642
SPT(14)	390592179116613689	0 8 18 20 24 50 78 80 108 134 138 140 150 158	58465993650
TPT(12)	390592180491246131	0 2 66 68 156 158 180 182 210 212 228 230	59840626092