Prime p₀= 1079717278175308271 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 46 2 28 2 10 2 28 2 46 2 (?)
a_n: 0 2 48 50 78 80 90 92 120 122 168 170
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: 170
Found by: Spectrum
db: batch=76, k=12, 2 46 2 28 2 10

SPT(16)	1079716212412857211	0 10 30 70 76 96 100 148 168 216 220 240 246 286 306 316	-1065762451060
SPT(16)	1079716291515919399	0 4 60 70 84 90 112 144 238 270 292 298 312 322 378 382	-986659388872
SPT(16)	1079716349545106963	0 30 44 68 98 110 114 120 218 224 228 240 270 294 308 338	-928630201308
STPT(10)	1079716870447331537	0 2 12 14 222 224 432 434 444 446	-407727976734
SPT(16)	1079717227454088679	0 22 42 52 84 88 102 108 124 130 144 148 180 190 210 232	-50721219592
SPT(16)	1079717259672010111	0 10 22 36 42 48 76 78 250 252 280 286 292 306 318 328	-18503298160
SPT(16)	1079717471603657951	0 38 50 78 116 126 150 182 186 218 242 252 290 318 330 368	193428349680
SPT(16)	1079718100211017963	0 40 66 78 100 124 148 150 154 156 180 204 226 238 264 304	822035709692
SPT(16)	1079718340183491997	0 4 22 52 60 72 84 106 150 172 184 196 204 234 252 256	1062008183726
SPT(16)	1079718386585818723	0 58 60 64 84 90 100 126 148 174 184 190 210 214 216 274	1108410510452
STPT(10)	1079718488111670107	0 2 30 32 42 44 54 56 84 86	1209936361836