Prime p₀= 1518424369719594497 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
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: 56
Found by: TheKillerChicken
db: batch=78, k=12, 2 10 2 10 2 4

SPT(16)	1518422719755731819	0 24 54 78 98 122 134 168 194 228 240 264 284 308 338 362	-1649963862678
SPT(16)	1518422994179656751	0 36 50 138 146 236 240 278 330 368 372 462 470 558 572 608	-1375539937746
SPT(16)	1518423026303914879	0 12 30 40 78 88 108 120 130 142 162 172 210 220 238 250	-1343415679618
STPT(10)	1518423509978270801	0 2 6 8 48 50 90 92 96 98	-859741323696
SPT(16)	1518423779898681041	0 50 60 68 86 96 116 138 140 162 182 192 210 218 228 278	-589820913456
SPT(16)	1518424139573313853	0 24 30 34 58 84 118 124 144 150 184 210 234 238 244 268	-230146280644
STPT(10)	1518424424910906839	0 2 18 20 30 32 42 44 60 62	55191312342
TPT(14)	1518424652309938559	0 2 30 32 90 92 102 104 132 134 222 224 258 260	282590344062
STPT(10)	1518425064414713051	0 2 36 38 78 80 120 122 156 158	694695118554
TPT(14)	1518425153995500869	0 2 42 44 60 62 138 140 198 200 222 224 228 230	784275906372
SPT(16)	1518425399397497009	0 14 38 42 44 60 74 80 132 138 152 168 170 174 198 212	1029677902512