Prime p₀= 2561166465402262517 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 16 2 10 2 16 2 40 2 (?)
a_n: 0 2 42 44 60 62 72 74 90 92 132 134
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: 134
Found by: JayPi
db: batch=82, k=12, 2 40 2 16 2 10

SPT(16)	2561165526377573233	0 6 18 30 66 70 76 88 96 108 114 118 154 166 178 184	-939024689284
STPT(10)	2561165577963343397	0 2 54 56 72 74 90 92 144 146	-887438919120
SPT(16)	2561165891165780267	0 42 54 56 62 80 96 102 224 230 246 264 270 272 284 326	-574236482250
SPT(16)	2561165965196453773	0 16 28 60 70 138 148 184 210 246 256 324 334 366 378 394	-500205808744
SPT(16)	2561166105732521123	0 18 36 104 170 246 258 260 264 266 278 354 420 488 506 524	-359669741394
SPT(20)	2561166381709028759	0 2 12 24 32 54 72 98 150 168 194 212 264 290 308 330 338 350 360 362	-83693233758
SPT(16)	2561166755307984613	0 4 6 10 70 88 108 124 270 286 306 324 384 388 390 394	289905722096
SPT(16)	2561166828978005429	0 2 42 48 62 80 110 128 192 210 240 258 272 278 318 320	363575742912
STPT(10)	2561166854243830871	0 2 96 98 108 110 120 122 216 218	388841568354
SPT(16)	2561166967518881999	0 14 68 92 110 134 144 210 212 278 288 312 330 354 408 422	502116619482
SPT(16)	2561167324831624877	0 14 32 90 120 132 144 146 210 212 224 236 266 324 342 356	859429362360