Prime p₀= 2373830283970591517 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: Landjunge
db: batch=81, k=12, 2 10 2 10 2 4

SPT(16)	2373829421440438343	0 18 56 78 110 120 128 156 158 186 194 204 236 258 296 314	-862530153174
TPT(14)	2373829490635770899	0 2 12 14 30 32 180 182 210 212 240 242 312 314	-793334820618
STPT(10)	2373829590410357657	0 2 30 32 42 44 54 56 84 86	-693560233860
TPT(14)	2373829726675860419	0 2 30 32 42 44 72 74 108 110 180 182 198 200	-557294731098
SPT(16)	2373829987524107501	0 2 30 86 98 120 140 156 272 288 308 330 342 398 426 428	-296446484016
SPT(16)	2373830081059422347	0 14 24 66 84 96 104 162 164 222 230 242 260 302 312 326	-202911169170
SPT(16)	2373830371665947687	0 12 86 122 132 182 192 194 252 254 264 314 324 360 434 446	87695356170
STPT(10)	2373830623452427619	0 2 18 20 30 32 42 44 60 62	339481836102
STPT(10)	2373830673840480857	0 2 30 32 60 62 90 92 120 122	389869889340
SPT(16)	2373830985010170857	0 26 36 54 72 96 110 176 210 276 290 314 332 350 360 386	701039579340
TPT(14)	2373831049366368407	0 2 30 32 72 74 102 104 114 116 252 254 270 272	765395776890