Prime p₀= 2391608032313194127 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 166 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 210 212 240 242 252 254
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: 254
Found by: Conan
db: batch=81, k=12, 2 10 2 28 2 166

TPT(14)	2391606655004737979	0 2 72 74 90 92 180 182 198 200 228 230 240 242	-1377308456148
STPT(10)	2391606679464247769	0 2 18 20 30 32 42 44 60 62	-1352848946358
SPT(16)	2391606693736213337	0 14 26 62 126 234 236 242 264 270 272 380 444 480 492 506	-1338576980790
SPT(16)	2391606929643107051	0 2 12 38 80 116 126 128 150 152 162 198 240 266 276 278	-1102670087076
STPT(10)	2391607217555927489	0 2 18 20 30 32 42 44 60 62	-814757266638
SPT(16)	2391607373984639207	0 12 66 122 176 182 204 222 314 332 354 360 414 470 524 536	-658328554920
SPT(16)	2391608199876351319	0 12 22 34 42 90 94 100 174 180 184 232 240 252 262 274	167563157192
TPT(14)	2391608226356375357	0 2 60 62 132 134 144 146 210 212 300 302 342 344	194043181230
STPT(10)	2391608586287315951	0 2 6 8 48 50 90 92 96 98	553974121824
STPT(10)	2391608725123896041	0 2 30 32 78 80 126 128 156 158	692810701914
SPT(16)	2391608734765146877	0 54 82 96 100 112 142 166 180 204 234 246 250 264 292 346	702451952750