Prime p₀= 2367820633864172939 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 40 2 34 2 40 2 58 2 (?)
a_n: 0 2 60 62 102 104 138 140 180 182 240 242
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: 242
Found by: arkiss
db: batch=81, k=12, 2 58 2 40 2 34

SPT(16)	2367819604732934251	0 70 72 82 96 100 118 130 198 210 228 232 246 256 258 328	-1029131238688
STPT(10)	2367819655370550551	0 2 30 32 78 80 126 128 156 158	-978493622388
SPT(16)	2367819682607534957	0 86 140 156 162 174 194 200 366 372 392 404 410 426 480 566	-951256637982
SPT(16)	2367819846026248711	0 6 10 66 88 132 136 226 252 342 346 390 412 468 472 478	-787837924228
STPT(10)	2367819969273997499	0 2 18 20 30 32 42 44 60 62	-664590175440
TPT(14)	2367820086066029261	0 2 6 8 30 32 78 80 120 122 186 188 216 218	-547798143678
SPT(16)	2367820916803997197	0 4 30 46 96 100 114 144 196 226 240 244 294 310 336 340	282939824258
SPT(16)	2367820989138037999	0 30 60 90 100 102 108 150 262 304 310 312 322 352 382 412	355273865060
SPT(16)	2367821377694470421	0 20 36 38 42 78 80 96 122 138 140 176 180 182 198 218	743830297482
STPT(10)	2367821474912083427	0 2 12 14 42 44 72 74 84 86	841047910488
STPT(12)	2367821557067810537	0 2 12 14 72 74 150 152 210 212 222 224	923203637598