Prime p₀= 2678665200880090757 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: JayPi
db: batch=82, k=12, 2 22 2 4 2 22

SPT(16)	2678664007017329911	0 46 52 82 108 112 118 126 142 150 156 160 186 216 222 268	-1193862760846
STPT(10)	2678664176302814801	0 2 6 8 48 50 90 92 96 98	-1024577275956
STPT(10)	2678664774490478099	0 2 18 20 30 32 42 44 60 62	-426389612658
STPT(10)	2678664974230507727	0 2 54 56 192 194 330 332 384 386	-226649583030
STPT(10)	2678665081299981227	0 2 24 26 42 44 60 62 84 86	-119580109530
SPT(16)	2678665180839650567	0 96 102 104 144 146 174 180 236 242 270 272 312 314 320 416	-20040440190
STPT(10)	2678665216809591431	0 2 36 38 78 80 120 122 156 158	15929500674
SPT(16)	2678665242164647819	0 4 10 12 70 94 100 114 208 222 228 252 310 312 318 322	41284557062
SPT(16)	2678665420747024223	0 6 54 78 104 120 126 128 186 188 194 210 236 260 308 314	219866933466
SPT(16)	2678665454688786769	0 34 72 82 84 174 202 204 280 282 310 400 402 412 450 484	253808696012
SPT(16)	2678665893792600167	0 32 42 74 102 140 144 164 240 260 264 302 330 362 372 404	692912509410