Prime p₀= 779043117770709809 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 46 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 90 92 120 122 132 134
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 10 2 28 2 46

SPT(13)	779041296050277109	0 24 48 84 90 108 174 240 258 264 300 324 348	-1821720432700
SPT(16)	779042338769782069	0 24 54 90 160 202 222 234 310 322 342 384 454 490 520 544	-779000927740
SPT(16)	779042666818156841	0 2 66 72 116 126 140 150 182 192 206 216 260 266 330 332	-450952552968
STPT(10)	779042673721548989	0 2 18 20 30 32 42 44 60 62	-444049160820
SPT(16)	779042768084998541	0 36 60 62 66 122 132 150 218 236 246 302 306 308 332 368	-349685711268
SPT(16)	779042773309540451	0 18 26 50 78 96 110 126 242 258 272 290 318 342 350 368	-344461169358
SPT(16)	779043459144134581	0 12 28 48 60 88 108 126 172 190 210 238 250 270 286 298	341373424772
SPT(16)	779043616065612299	0 30 54 62 98 114 128 264 308 444 458 474 510 518 542 572	498294902490
STPT(10)	779043727419186137	0 2 30 32 42 44 54 56 84 86	609648476328
STPT(10)	779044181785747247	0 2 30 32 42 44 54 56 84 86	1064015037438
SPT(16)	779044291997145641	0 8 62 90 98 108 132 140 210 218 242 252 260 288 342 350	1174226435832