Prime p₀= 2394683044826502317 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 22 2 4 2 22 2 4 2 22 2 (?)
a_n: 0 2 24 26 30 32 54 56 60 62 84 86
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: 86
Found by: Landjunge
db: batch=81, k=12, 2 22 2 4 2 22

SPT(16)	2394681966149767867	0 4 24 42 84 124 150 172 264 286 312 352 394 412 432 436	-1078676734450
SPT(16)	2394681970853861023	0 10 24 48 88 96 124 136 168 180 208 216 256 280 294 304	-1073972641294
STPT(12)	2394682219448646227	0 2 42 44 60 62 84 86 102 104 144 146	-825377856090
SPT(16)	2394682504664159383	0 34 36 46 70 108 130 144 160 174 196 234 258 268 270 304	-540162342934
STPT(10)	2394682629658689911	0 2 30 32 78 80 126 128 156 158	-415167812406
SPT(16)	2394682718736601807	0 22 24 34 90 94 126 132 154 160 192 196 252 262 264 286	-326089900510
TPT(14)	2394683055264016079	0 2 12 14 90 92 138 140 162 164 252 254 258 260	10437513762
TPT(14)	2394683337690690017	0 2 30 32 72 74 102 104 114 116 210 212 252 254	292864187700
SPT(16)	2394684062930329397	0 36 44 50 62 96 120 126 140 146 170 204 216 222 230 266	1018103827080
STPT(10)	2394684274302527189	0 2 48 50 90 92 132 134 180 182	1229476024872
STPT(10)	2394684330817554869	0 2 18 20 30 32 42 44 60 62	1285991052552