Prime p₀= 2428572752947856609 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 34 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 78 80 108 110 120 122
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: [SG-FC] hl
db: batch=82, k=12, 2 10 2 28 2 34

SPT(16)	2428571330048417263	0 6 30 54 58 64 78 84 190 196 210 216 220 244 268 274	-1422899439346
STPT(10)	2428571653304595941	0 2 6 8 18 20 30 32 36 38	-1099643260668
SPT(16)	2428571826236257847	0 14 60 104 134 192 236 264 272 300 344 402 432 476 522 536	-926711598762
STPT(10)	2428571952089788157	0 2 42 44 102 104 162 164 204 206	-800858068452
STPT(12)	2428572131601346481	0 2 36 38 48 50 78 80 90 92 126 128	-621346510128
SPT(16)	2428572401956604003	0 14 36 48 74 78 80 84 140 144 146 150 176 188 210 224	-350991252606
SPT(16)	2428572951407622869	0 20 44 48 62 98 132 150 152 170 204 240 254 258 282 302	198459766260
STPT(10)	2428572994129779851	0 2 6 8 48 50 90 92 96 98	241181923242
SPT(16)	2428573358072193649	0 28 42 48 94 102 114 118 144 148 160 168 214 220 234 262	605124337040
STPT(10)	2428574214802328009	0 2 18 20 30 32 42 44 60 62	1461854471400
STPT(10)	2428574414512219397	0 2 12 14 72 74 132 134 144 146	1661564362788