Prime p₀= 2267177696112506027 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 22 2 34 2 22 2 28 2 (?)
a_n: 0 2 30 32 54 56 90 92 114 116 144 146
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: 146
Found by: Orange Kid
db: batch=81, k=12, 2 28 2 22 2 34

SPT(16)	2267176892286757219	0 10 42 52 60 70 82 150 172 240 252 262 270 280 312 322	-803825748808
STPT(10)	2267177127226862309	0 2 18 20 30 32 42 44 60 62	-568885643718
STPT(10)	2267177158074187517	0 2 54 56 72 74 90 92 144 146	-538038318510
SPT(16)	2267177380908117133	0 16 30 46 58 60 96 124 240 268 304 306 318 334 348 364	-315204388894
SPT(16)	2267177394957636373	0 4 10 28 84 94 108 160 168 220 234 244 300 318 324 328	-301154869654
STPT(10)	2267177492020938851	0 2 6 8 48 50 90 92 96 98	-204091567176
SPT(16)	2267177759703279581	0 72 78 86 92 138 210 240 308 338 410 456 462 470 476 548	63590773554
STPT(10)	2267177887120742159	0 2 168 170 210 212 252 254 420 422	191008236132
SPT(16)	2267178693470501711	0 6 20 66 80 90 98 116 132 150 158 168 182 228 242 248	997357995684
STPT(10)	2267178911847956177	0 2 30 32 42 44 54 56 84 86	1215735450150
SPT(16)	2267179044690880751	0 6 30 60 68 72 126 176 222 272 326 330 338 368 392 398	1348578374724