Prime p₀= 1069857705395353811 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 28 2 4 2 28 2 28 2 (?)
a_n: 0 2 30 32 60 62 66 68 96 98 126 128
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: 128
Found by: arkiss
db: batch=76, k=12, 2 28 2 28 2 4

SPT(16)	1069856081827063339	0 54 112 162 174 198 238 282 340 384 424 448 460 510 568 622	-1623568290472
SPT(16)	1069856085652165921	0 18 30 90 118 132 148 172 198 222 238 252 280 340 352 370	-1619743187890
SPT(16)	1069856142082022783	0 14 20 24 36 66 104 140 174 210 248 278 290 294 300 314	-1563313331028
STPT(10)	1069857125551626257	0 2 24 26 42 44 60 62 84 86	-579843727554
STPT(10)	1069857313661445467	0 2 12 14 72 74 132 134 144 146	-391733908344
SPT(16)	1069857598600541533	0 6 34 100 118 150 154 198 256 300 304 336 354 420 448 454	-106794812278
TPT(14)	1069857836689663421	0 2 36 38 168 170 180 182 240 242 246 248 306 308	131294309610
SPT(20)	1069858583584597589	0 32 54 80 84 90 102 104 138 150 182 194 228 230 242 248 252 278 300 332	878189243778
STPT(10)	1069858699037151767	0 2 42 44 72 74 102 104 144 146	993641797956
SPT(16)	1069858766694492647	0 14 54 92 110 132 134 164 192 222 224 246 264 302 342 356	1061299138836
STPT(10)	1069858843126256387	0 2 12 14 42 44 72 74 84 86	1137730902576