Prime p₀= 2005889959919721917 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 10 2 4 2 10 2 40 2 (?)
a_n: 0 2 42 44 54 56 60 62 72 74 114 116
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: 116
Found by: vaughan
db: batch=80, k=12, 2 40 2 10 2 4

SPT(16)	2005888490709143281	0 28 42 70 90 112 148 150 178 180 216 238 258 286 300 328	-1469210578636
STPT(10)	2005889062362056477	0 2 12 14 72 74 132 134 144 146	-897557665440
STPT(10)	2005889151795802919	0 2 48 50 60 62 72 74 120 122	-808123918998
STPT(10)	2005889390404211339	0 2 18 20 30 32 42 44 60 62	-569515510578
SPT(16)	2005889436633267047	0 20 30 42 140 144 156 162 254 260 272 276 374 386 396 416	-523286454870
SPT(16)	2005889862365106269	0 2 14 24 48 54 68 102 110 144 158 164 188 198 210 212	-97554615648
STPT(10)	2005890274194007109	0 2 18 20 30 32 42 44 60 62	314274285192
SPT(16)	2005890452227896931	0 58 76 82 120 162 168 198 250 280 286 328 366 372 390 448	492308175014
STPT(10)	2005890768824032817	0 2 24 26 42 44 60 62 84 86	808904310900
SPT(16)	2005890863608195049	0 12 14 50 72 110 134 140 162 168 192 230 252 288 290 302	903688473132
SPT(16)	2005891088270911111	0 28 40 78 138 142 196 222 226 252 306 310 370 408 420 448	1128351189194