Prime p₀= 2678630179395351239 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 58 2 28 2 76 2 28 2 58 2 (?)
a_n: 0 2 60 62 90 92 168 170 198 200 258 260
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: 260
Found by: [SG-FC] hl
db: batch=82, k=12, 2 58 2 28 2 76

SPT(16)	2678628144279485639	0 20 38 50 54 104 132 134 138 140 168 218 222 234 252 272	-2035115865600
SPT(16)	2678628203696011499	0 44 62 72 78 80 170 174 248 252 342 344 350 360 378 422	-1975699339740
SPT(16)	2678628293966631739	0 10 12 52 64 78 82 84 88 90 94 108 120 160 162 172	-1885428719500
SPT(16)	2678628334776625333	0 36 46 76 126 174 186 196 264 274 286 334 384 414 424 460	-1844618725906
SPT(18)	2678628363948287197	0 40 46 54 84 124 126 156 192 214 250 280 282 322 352 360 366 406	-1815447064042
SPT(16)	2678629490569822459	0 4 10 18 42 54 60 130 132 202 208 220 244 252 258 262	-688825528780
STPT(10)	2678630474659883057	0 2 30 32 72 74 114 116 144 146	295264531818
STPT(10)	2678630562894230507	0 2 54 56 132 134 210 212 264 266	383498879268
SPT(16)	2678630988550198037	0 2 14 110 152 182 224 240 296 312 354 384 426 522 534 536	809154846798
TPT(14)	2678631228807538091	0 2 66 68 90 92 126 128 150 152 216 218 336 338	1049412186852
STPT(12)	2678631228807538091	0 2 66 68 90 92 126 128 150 152 216 218	1049412186852