Prime p₀= 772810694478417599 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 10 2 46 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 90 92 102 104 132 134
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: 134
Found by: scrap
db: batch=73, k=12, 2 28 2 10 2 46

SPT(16)	772809455942796539	0 12 42 68 72 80 122 150 182 210 252 260 264 290 320 332	-1238535621060
SPT(16)	772809485774959667	0 6 12 26 110 140 180 210 212 242 282 312 396 410 416 422	-1208703457932
STPT(10)	772809618961105931	0 2 6 8 18 20 30 32 36 38	-1075517311668
SPT(16)	772809740037704507	0 6 12 56 62 80 102 150 266 314 336 354 360 404 410 416	-954440713092
SPT(16)	772810518291020747	0 14 30 42 62 104 132 146 180 194 222 264 284 296 312 326	-176187396852
SPT(16)	772810560447930649	0 10 12 30 42 52 54 88 204 238 240 250 262 280 282 292	-134030486950
STPT(10)	772811362018617707	0 2 30 32 60 62 90 92 120 122	667540200108
STPT(10)	772811375879212847	0 2 60 62 102 104 144 146 204 206	681400795248
STPT(10)	772811503750025807	0 2 12 14 72 74 132 134 144 146	809271608208
STPT(10)	772811682742579937	0 2 30 32 72 74 114 116 144 146	988264162338
STPT(10)	772811836956163097	0 2 30 32 60 62 90 92 120 122	1142477745498