Prime p₀= 2123548009497727907 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 52 2 28 2 34 2 28 2 52 2 (?)
a_n: 0 2 54 56 84 86 120 122 150 152 204 206
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: 206
Found by: Chooka
db: batch=80, k=12, 2 52 2 28 2 34

SPT(16)	2123547427881454543	0 24 66 78 106 196 216 220 234 238 258 348 376 388 430 454	-581616273364
STPT(10)	2123547639149512349	0 2 12 14 90 92 168 170 180 182	-370348215558
SPT(16)	2123547708409591733	0 66 78 98 146 176 188 246 260 318 330 360 408 428 440 506	-301088136174
STPT(10)	2123547752903647151	0 2 6 8 48 50 90 92 96 98	-256594080756
STPT(10)	2123547994960401167	0 2 30 32 72 74 114 116 144 146	-14537326740
TPT(14)	2123548009497727871	0 2 36 38 90 92 120 122 156 158 186 188 240 242	-36
SPT(16)	2123548145602066649	0 12 30 72 102 140 174 188 264 278 312 350 380 422 440 452	136104338742
SPT(16)	2123548271930770903	0 36 60 70 78 106 136 148 168 180 210 238 246 256 280 316	262433042996
STPT(10)	2123548369936954559	0 2 18 20 30 32 42 44 60 62	360439226652
SPT(16)	2123548387066676359	0 40 60 108 130 144 234 240 292 298 388 402 424 472 492 532	377568948452
SPT(16)	2123548658596578043	0 36 54 78 136 150 168 204 250 286 304 318 376 400 418 454	649098850136