Prime p₀= 2564489048505602159 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 70 2 4 2 70 2 58 2 (?)
a_n: 0 2 60 62 132 134 138 140 210 212 270 272
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: 272
Found by: [SG-FC] hl
db: batch=82, k=12, 2 58 2 70 2 4

SPT(16)	2564488288071110461	0 36 130 166 196 210 228 238 240 250 268 282 312 348 442 478	-760434491698
STPT(10)	2564488355553382931	0 2 30 32 78 80 126 128 156 158	-692952219228
SPT(16)	2564488617259667629	0 4 18 48 58 60 70 82 90 102 112 114 124 154 168 172	-431245934530
STPT(10)	2564488625138717411	0 2 36 38 78 80 120 122 156 158	-423366884748
SPT(16)	2564488765870974841	0 6 40 42 70 82 90 136 156 202 210 222 250 252 286 292	-282634627318
STPT(10)	2564488928313819467	0 2 30 32 102 104 174 176 204 206	-120191782692
SPT(16)	2564489418482173771	0 30 36 58 70 72 130 142 156 168 226 228 240 262 268 298	369976571612
SPT(16)	2564489448128947121	0 30 60 122 132 170 188 198 200 210 228 266 276 338 368 398	399623344962
STPT(10)	2564489864682067757	0 2 30 32 42 44 54 56 84 86	816176465598
STPT(10)	2564490329719707419	0 2 18 20 30 32 42 44 60 62	1281214105260
STPT(10)	2564490741029114837	0 2 30 32 60 62 90 92 120 122	1692523512678