Prime p₀= 2768857671615355589 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 76 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 120 122 150 152 162 164
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: 164
Found by: [SG-FC] hl
db: batch=82, k=12, 2 10 2 28 2 76

SPT(16)	2768856484988892601	0 28 42 52 70 78 102 142 198 238 262 270 288 298 312 340	-1186626462988
SPT(16)	2768856488084225797	0 42 124 154 172 196 202 214 222 234 240 264 282 312 394 436	-1183531129792
SPT(16)	2768856612184727303	0 24 30 98 114 116 150 194 210 254 288 290 306 374 380 404	-1059430628286
SPT(16)	2768856894238327817	0 26 42 66 80 84 92 96 140 144 152 156 170 194 210 236	-777377027772
SPT(16)	2768857328525020261	0 6 36 40 46 60 112 126 292 306 358 372 378 382 412 418	-343090335328
STPT(10)	2768857371497515229	0 2 42 44 120 122 198 200 240 242	-300117840360
STPT(10)	2768857730757458309	0 2 12 14 30 32 48 50 60 62	59142102720
STPT(10)	2768858110506751127	0 2 42 44 72 74 102 104 144 146	438891395538
STPT(10)	2768858126378614799	0 2 12 14 90 92 168 170 180 182	454763259210
STPT(10)	2768858341940626877	0 2 30 32 42 44 54 56 84 86	670325271288
SPT(16)	2768858443075722089	0 14 44 158 228 264 374 378 404 408 518 554 624 738 768 782	771460366500