Prime p₀= 1459870449624641081 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: Theadalus
db: batch=78, k=12, 2 28 2 28 2 4

SPT(16)	1459868615384680957	0 16 54 66 96 126 172 184 222 234 280 310 340 352 390 406	-1834239960124
SPT(16)	1459868974114208491	0 22 40 60 78 100 162 168 250 256 318 340 358 378 396 418	-1475510432590
SPT(16)	1459869047318441329	0 30 64 70 72 78 82 84 148 150 154 160 162 168 202 232	-1402306199752
STPT(10)	1459869305670801209	0 2 18 20 30 32 42 44 60 62	-1143953839872
SPT(16)	1459869488457759649	0 22 48 84 100 132 138 160 162 184 190 222 238 274 300 322	-961166881432
STPT(10)	1459869632346840467	0 2 54 56 132 134 210 212 264 266	-817277800614
STPT(10)	1459870930903099019	0 2 42 44 90 92 138 140 180 182	481278457938
TPT(14)	1459871128102283291	0 2 180 182 378 380 456 458 468 470 498 500 570 572	678477642210
TPT(16)	1459871271716759507	0 2 12 14 72 74 90 92 144 146 210 212 240 242 474 476	822092118426
TPT(14)	1459871517224764079	0 2 18 20 42 44 120 122 168 170 252 254 258 260	1067600122998
STPT(10)	1459871675545042547	0 2 60 62 72 74 84 86 144 146	1225920401466