Prime p₀= 2066780509473200579 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 34 2 52 2 34 2 40 2 (?)
a_n: 0 2 42 44 78 80 132 134 168 170 210 212
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: 212
Found by: Cruncher Pete
db: batch=80, k=12, 2 40 2 34 2 52

SPT(16)	2066779952880355187	0 24 44 66 90 102 116 132 164 180 194 206 230 252 272 296	-556592845392
STPT(10)	2066780171869138907	0 2 30 32 42 44 54 56 84 86	-337604061672
STPT(10)	2066780266497949127	0 2 30 32 72 74 114 116 144 146	-242975251452
SPT(16)	2066780377090600429	0 4 34 42 52 114 124 154 198 228 238 300 310 318 348 352	-132382600150
SPT(16)	2066780417412581357	0 50 54 56 90 146 186 222 224 260 300 356 390 392 396 446	-92060619222
STPT(10)	2066780443674679919	0 2 18 20 30 32 42 44 60 62	-65798520660
SPT(16)	2066781005835437819	0 48 54 74 90 102 114 120 152 158 170 182 198 218 224 272	496362237240
SPT(16)	2066781186924214909	0 10 12 40 54 70 82 114 148 180 192 208 222 250 252 262	677451014330
SPT(16)	2066781234100963147	0 10 42 52 76 82 94 132 214 252 264 270 294 304 336 346	724627762568
STPT(10)	2066781251314634681	0 2 30 32 78 80 126 128 156 158	741841434102
TPT(14)	2066781750183394247	0 2 24 26 90 92 120 122 174 176 234 236 252 254	1240710193668